-
Natural Logarithms
This algebra video tutorial provides a basic introduction into natural logarithms. It explains how to evaluate natural logarithmic expressions with the natural base e and how to evaluate exponential expressions with natural logs in on the exponent of the natural base e using properties of logarithms.
Logarithms - The Easy Way!
https://www.youtube.com/watch?v=kqVpPSzkTYA
Log to Exponential Form:
https://www.youtube.com/watch?v=f0C1KL7GkqY
Change of Base Formula:
https://www.youtube.com/watch?v=FFm-zaFW_X4
Change of Base Log Problem:
https://www.youtube.com/watch?v=p7hD9VdXv9U
Properties of Logarithms:
https://www.youtube.c...
published: 31 Jan 2018
-
What are natural logarithms and their properties
👉 Learn all about the properties of logarithms. The logarithm of a number say a to the base of another number say b is a number say n which when raised as a power of b gives a. (i.e. log [base b] (a) = n means that b^n = a). The logarithm of a negative number is not defined. (i.e. it is not possible to find the logarithm of a negative number). There are some properties of logarithm which are helpful in simplifying and evaluating logarithm problems. Knowledge of these properties is a valuable tool in solving logarithm problems.
👏SUBSCRIBE to my channel here: https://www.youtube.com/user/mrbrianmclogan?sub_confirmation=1
❤️Support my channel by becoming a member: https://www.youtube.com/channel/UCQv3dpUXUWvDFQarHrS5P9A/join
🙋♂️Have questions? Ask here: https://forms.gle/dfR9HbCu6qpWbJdo...
published: 18 Sep 2013
-
What is e and ln(x)? (Euler's Number and The Natural Logarithm)
Euler's Number, e, is one of the most prominent constants in mathematics and exponential functions are some of the most important in maths. In this video: we take a deep dive into what Euler's Number is, what exponential functions are and how to differentiate them and we take a look at the super important natural logarithm, ln(x).
Website: http://mathacy.com
Timestamps:
0:00 - Intro
0:27 - Compound interest
2:37 - Defining e (Euler's Number)
3:30 - Differentiating exponential functions
6:10 - Derivative of e^x
6:48 - The Natural Logarithm - ln(x)
8:22 - Derivative of ln(x)
published: 17 Jan 2021
-
The History of the Natural Logarithm - How was it discovered?
- Learning about the history of the natural logarithm helps us understand what it is.
Today we define the natural logarithm as a logarithm with the base e and many people, understandably, wonder why! Interestingly the natural logarithm was discovered decades before the number e. In fact it was discovered before the link between logarithms and exponentials was recognized!
In this video I talk about how and why logarithms were invented, how the natural logarithm arise from from logarithmic tables without the need of the number e and how studying the area of the hyperbola was instrumental in defining logarithms and the natural logarithm.
Support this channel
Your support of the channel is very much appreciated. You can do so at the links below. Thanks for keeping me going :)
- Buy me a c...
published: 04 Mar 2022
-
Natural Logarithms
Find a local tutor in you area now! Get homework help now! FREE online Tutoring on Thursday nights! All FREE @ http://textbooktactics.com
Click show more for Video Description:
Natural Logarithms: Introduction to natural logarithms, using log properties to simplify or expand natural logarithms, solving natural logarithms, and using natural logarithms to solve exponential equations with a natural base e.
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published: 24 May 2012
-
Defining the natural logarithm
The definition of the natural log as an area accumulation function. #shorts #math #manim #logarithms #calculus #integral
published: 25 Apr 2023
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What makes the natural log "natural"? | Ep. 7 Lockdown live math
All about ln(x).
Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev
Home page: https://www.3blue1brown.com
Brought to you by you: https://3b1b.co/ldm-thanks
Beautiful pictorial summary by @ThuyNganVu:
https://twitter.com/ThuyNganVu/status/1259288683489849344
Errors:
At minute 16, the sum should be written with a "..." to indicate going to infinity.
At minute 38, the exponent should have 1/(2s^2) instead of 1/s^2 for s to represent standard deviation.
At minute 54, an equal sign was mistakenly used in taking the derivative of x^3 / 3!.
At the end, it should be pointed out that the alternating series with x^n terms only converges for values of x between -1 and 1, so the values one can't be considered proven with values of x outside that range. Everythi...
published: 08 May 2020
-
The Exponential Function e and The Natural Log ln
A Level Maths revision tutorial video.
For the full list of videos and more revision resources visit www.mathsgenie.co.uk.
published: 12 Sep 2017
-
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Welcome to your private log home retreat, nestled along the river next to Bowness Park—a sanctuary where history and nature harmoniously converge. This captivating residence showcases hand-hewn Norwegian-style logs that have aged beautifully, providing natural insulation for cozy winters and cool summers.
Approaching the home, you are greeted by an inviting front porch—perfect for morning coffees or relaxing evenings—a charming introduction to this special abode. Situated on a 50’x482’, 0.55-acre lot, the property ensures complete privacy amidst a forested landscape teeming with wildlife and a serene creek in the backyard.
Step inside to discover a captivating interior. The sunken living room boasts 25-foot open-beam cathedral ceilings and a high-efficiency MORSO stove, offering a cozy r...
published: 29 Jun 2024
-
Logarithms... How? (NancyPi)
MIT grad introduces logs and shows how to evaluate them. To skip ahead: 1) For how to understand and evaluate BASIC LOGS, skip to time 0:52. 2) For how to evaluate weirder logs, including the log of 0, 1, a FRACTION, or a NEGATIVE number, skip to time 6:44. 3) For NATURAL LOGS (LN X), skip to time 11:17. 4) For even weirder logs, including SOLVING for X and using the CHANGE-OF-BASE formula, skip to time 14:56. Nancy formerly of MathBFF explains the steps.
Follow Nancy on Instagram: https://instagram.com/nancypi
Twitter: https://twitter.com/nancypi
1) BASIC LOGS: you can read log notation as "log, base 3, of 9 equals X". The small (subscript) number is called the base. You can always evaluate a log expression by rearranging it into something called exponential form. Every log expression i...
published: 19 Aug 2018
2:49
Natural Logarithms
This algebra video tutorial provides a basic introduction into natural logarithms. It explains how to evaluate natural logarithmic expressions with the natural...
This algebra video tutorial provides a basic introduction into natural logarithms. It explains how to evaluate natural logarithmic expressions with the natural base e and how to evaluate exponential expressions with natural logs in on the exponent of the natural base e using properties of logarithms.
Logarithms - The Easy Way!
https://www.youtube.com/watch?v=kqVpPSzkTYA
Log to Exponential Form:
https://www.youtube.com/watch?v=f0C1KL7GkqY
Change of Base Formula:
https://www.youtube.com/watch?v=FFm-zaFW_X4
Change of Base Log Problem:
https://www.youtube.com/watch?v=p7hD9VdXv9U
Properties of Logarithms:
https://www.youtube.com/watch?v=Jtv9Lnf7Zw8
____________________________________
Expanding Logarithmic Expressions:
https://www.youtube.com/watch?v=OIz-5MyJA3g
Condensing Logarithmic Expressions:
https://www.youtube.com/watch?v=luRrOlsB4cY
Natural Logarithms:
https://www.youtube.com/watch?v=daUlTsnCNRQ
Solving Exponential Equations:
https://www.youtube.com/watch?v=9tutJ5xrRwg
Exponential Equations - Quadratic Form:
https://www.youtube.com/watch?v=yNgmVu0R_T8
_______________________________________
Solving Logarithmic Equations:
https://www.youtube.com/watch?v=fnhFneOz6n8
Graphing Logarithmic Functions:
https://www.youtube.com/watch?v=-nptxS9rZNA
Graphing Exponential Functions:
https://www.youtube.com/watch?v=DASfP8KAyvs
Compound Interest Word Problems:
https://www.youtube.com/watch?v=Hn0eLcOSQGw
Logarithms Practice Problems:
https://www.youtube.com/watch?v=7DVbQKI600k
_______________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/
Full-Length Videos and Worksheets:
https://www.patreon.com/MathScienceTutor/collections
https://wn.com/Natural_Logarithms
This algebra video tutorial provides a basic introduction into natural logarithms. It explains how to evaluate natural logarithmic expressions with the natural base e and how to evaluate exponential expressions with natural logs in on the exponent of the natural base e using properties of logarithms.
Logarithms - The Easy Way!
https://www.youtube.com/watch?v=kqVpPSzkTYA
Log to Exponential Form:
https://www.youtube.com/watch?v=f0C1KL7GkqY
Change of Base Formula:
https://www.youtube.com/watch?v=FFm-zaFW_X4
Change of Base Log Problem:
https://www.youtube.com/watch?v=p7hD9VdXv9U
Properties of Logarithms:
https://www.youtube.com/watch?v=Jtv9Lnf7Zw8
____________________________________
Expanding Logarithmic Expressions:
https://www.youtube.com/watch?v=OIz-5MyJA3g
Condensing Logarithmic Expressions:
https://www.youtube.com/watch?v=luRrOlsB4cY
Natural Logarithms:
https://www.youtube.com/watch?v=daUlTsnCNRQ
Solving Exponential Equations:
https://www.youtube.com/watch?v=9tutJ5xrRwg
Exponential Equations - Quadratic Form:
https://www.youtube.com/watch?v=yNgmVu0R_T8
_______________________________________
Solving Logarithmic Equations:
https://www.youtube.com/watch?v=fnhFneOz6n8
Graphing Logarithmic Functions:
https://www.youtube.com/watch?v=-nptxS9rZNA
Graphing Exponential Functions:
https://www.youtube.com/watch?v=DASfP8KAyvs
Compound Interest Word Problems:
https://www.youtube.com/watch?v=Hn0eLcOSQGw
Logarithms Practice Problems:
https://www.youtube.com/watch?v=7DVbQKI600k
_______________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/
Full-Length Videos and Worksheets:
https://www.patreon.com/MathScienceTutor/collections
- published: 31 Jan 2018
- views: 1285568
4:12
What are natural logarithms and their properties
👉 Learn all about the properties of logarithms. The logarithm of a number say a to the base of another number say b is a number say n which when raised as a pow...
👉 Learn all about the properties of logarithms. The logarithm of a number say a to the base of another number say b is a number say n which when raised as a power of b gives a. (i.e. log [base b] (a) = n means that b^n = a). The logarithm of a negative number is not defined. (i.e. it is not possible to find the logarithm of a negative number). There are some properties of logarithm which are helpful in simplifying and evaluating logarithm problems. Knowledge of these properties is a valuable tool in solving logarithm problems.
👏SUBSCRIBE to my channel here: https://www.youtube.com/user/mrbrianmclogan?sub_confirmation=1
❤️Support my channel by becoming a member: https://www.youtube.com/channel/UCQv3dpUXUWvDFQarHrS5P9A/join
🙋♂️Have questions? Ask here: https://forms.gle/dfR9HbCu6qpWbJdo7
🎉Follow the Community: https://www.youtube.com/user/MrBrianMcLogan/community
Organized Videos:
✅Evaluate Logarithms
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqLK5d-GnhbLJDu8HkQEaXH
✅Change of Base Formula
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrjV9ll7wRUGAwtBt3CVYAO
✅Rules of Logarithms
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMq5AvOOXsDWR7k_mcs0LvZo
✅Logarithms | Learn About
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMoGSEaJLND-_FZdxrV4m011
✅How to Evaluate Logarithms with Radicals
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpw2eSMrxI028RivTezW-O3
✅How to Evaluate Logarithms with Fractions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpyjKOkfXDoJPG7bT9rh3Q4
✅How to Evaluate Logarithms
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMreyyfjIh5QlfYp5_KSk90t
✅How to Evaluate Natural Logarithms
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMr1AzltBGBbmGLLR4y7fqHf
✅How to Evaluate Logarithmic Expressions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMoA-1oSX04rRpTu81FuVmse
🗂️ Organized playlists by classes here: https://www.youtube.com/user/MrBrianMcLogan/playlists
🌐 My Website - http://www.freemathvideos.com
🎯Survive Math Class Checklist: Ten Steps to a Better Year: https://www.brianmclogan.com/email-capture-fdea604e-9ee8-433f-aa93-c6fefdfe4d57
Connect with me:
⚡️Facebook - https://www.facebook.com/freemathvideos
⚡️Instagram - https://www.instagram.com/brianmclogan/
⚡️Twitter - https://twitter.com/mrbrianmclogan
⚡️Linkedin - https://www.linkedin.com/in/brian-mclogan-16b43623/
👨🏫 Current Courses on Udemy: https://www.udemy.com/user/brianmclogan2/
👨👩👧👧 About Me: I make short, to-the-point online math tutorials. I struggled with math growing up and have been able to use those experiences to help students improve in math through practical applications and tips. Find more here: https://www.freemathvideos.com/about-me/
#logarithmicfunctions #brianmclogan
https://wn.com/What_Are_Natural_Logarithms_And_Their_Properties
👉 Learn all about the properties of logarithms. The logarithm of a number say a to the base of another number say b is a number say n which when raised as a power of b gives a. (i.e. log [base b] (a) = n means that b^n = a). The logarithm of a negative number is not defined. (i.e. it is not possible to find the logarithm of a negative number). There are some properties of logarithm which are helpful in simplifying and evaluating logarithm problems. Knowledge of these properties is a valuable tool in solving logarithm problems.
👏SUBSCRIBE to my channel here: https://www.youtube.com/user/mrbrianmclogan?sub_confirmation=1
❤️Support my channel by becoming a member: https://www.youtube.com/channel/UCQv3dpUXUWvDFQarHrS5P9A/join
🙋♂️Have questions? Ask here: https://forms.gle/dfR9HbCu6qpWbJdo7
🎉Follow the Community: https://www.youtube.com/user/MrBrianMcLogan/community
Organized Videos:
✅Evaluate Logarithms
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqLK5d-GnhbLJDu8HkQEaXH
✅Change of Base Formula
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrjV9ll7wRUGAwtBt3CVYAO
✅Rules of Logarithms
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMq5AvOOXsDWR7k_mcs0LvZo
✅Logarithms | Learn About
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMoGSEaJLND-_FZdxrV4m011
✅How to Evaluate Logarithms with Radicals
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpw2eSMrxI028RivTezW-O3
✅How to Evaluate Logarithms with Fractions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpyjKOkfXDoJPG7bT9rh3Q4
✅How to Evaluate Logarithms
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMreyyfjIh5QlfYp5_KSk90t
✅How to Evaluate Natural Logarithms
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMr1AzltBGBbmGLLR4y7fqHf
✅How to Evaluate Logarithmic Expressions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMoA-1oSX04rRpTu81FuVmse
🗂️ Organized playlists by classes here: https://www.youtube.com/user/MrBrianMcLogan/playlists
🌐 My Website - http://www.freemathvideos.com
🎯Survive Math Class Checklist: Ten Steps to a Better Year: https://www.brianmclogan.com/email-capture-fdea604e-9ee8-433f-aa93-c6fefdfe4d57
Connect with me:
⚡️Facebook - https://www.facebook.com/freemathvideos
⚡️Instagram - https://www.instagram.com/brianmclogan/
⚡️Twitter - https://twitter.com/mrbrianmclogan
⚡️Linkedin - https://www.linkedin.com/in/brian-mclogan-16b43623/
👨🏫 Current Courses on Udemy: https://www.udemy.com/user/brianmclogan2/
👨👩👧👧 About Me: I make short, to-the-point online math tutorials. I struggled with math growing up and have been able to use those experiences to help students improve in math through practical applications and tips. Find more here: https://www.freemathvideos.com/about-me/
#logarithmicfunctions #brianmclogan
- published: 18 Sep 2013
- views: 550770
12:02
What is e and ln(x)? (Euler's Number and The Natural Logarithm)
Euler's Number, e, is one of the most prominent constants in mathematics and exponential functions are some of the most important in maths. In this video: we ta...
Euler's Number, e, is one of the most prominent constants in mathematics and exponential functions are some of the most important in maths. In this video: we take a deep dive into what Euler's Number is, what exponential functions are and how to differentiate them and we take a look at the super important natural logarithm, ln(x).
Website: http://mathacy.com
Timestamps:
0:00 - Intro
0:27 - Compound interest
2:37 - Defining e (Euler's Number)
3:30 - Differentiating exponential functions
6:10 - Derivative of e^x
6:48 - The Natural Logarithm - ln(x)
8:22 - Derivative of ln(x)
https://wn.com/What_Is_E_And_Ln(X)_(Euler's_Number_And_The_Natural_Logarithm)
Euler's Number, e, is one of the most prominent constants in mathematics and exponential functions are some of the most important in maths. In this video: we take a deep dive into what Euler's Number is, what exponential functions are and how to differentiate them and we take a look at the super important natural logarithm, ln(x).
Website: http://mathacy.com
Timestamps:
0:00 - Intro
0:27 - Compound interest
2:37 - Defining e (Euler's Number)
3:30 - Differentiating exponential functions
6:10 - Derivative of e^x
6:48 - The Natural Logarithm - ln(x)
8:22 - Derivative of ln(x)
- published: 17 Jan 2021
- views: 603176
18:21
The History of the Natural Logarithm - How was it discovered?
- Learning about the history of the natural logarithm helps us understand what it is.
Today we define the natural logarithm as a logarithm with the base e and ...
- Learning about the history of the natural logarithm helps us understand what it is.
Today we define the natural logarithm as a logarithm with the base e and many people, understandably, wonder why! Interestingly the natural logarithm was discovered decades before the number e. In fact it was discovered before the link between logarithms and exponentials was recognized!
In this video I talk about how and why logarithms were invented, how the natural logarithm arise from from logarithmic tables without the need of the number e and how studying the area of the hyperbola was instrumental in defining logarithms and the natural logarithm.
Support this channel
Your support of the channel is very much appreciated. You can do so at the links below. Thanks for keeping me going :)
- Buy me a coffee: https://www.buymeacoffee.com/tareksaid
- Support me on PayPal: http://bit.ly/3FmhvEo
- Patreon: https://www.patreon.com/tareksaid
Corrections:
- 11:33 The name of the hyperbola is: "Rectangular Hyperbola" not "Square Hyperbola"
-12:36 I realised after publishing the video that the method I used was not the method that was used by Saint Vincent. For the original method by Saint Vincent check: https://www.jstor.org/stable/3620207
-15:13 Saint Vincent didn't make the connection with the logarithms, he only discovered that they areas are equal. It was de Sarasa who made the connection
Notes:
- 00:02 I am using the terms discovered and invented in a specific sense. “Discovered” when a mathematical idea was stumbled upon, while “invented” when it was created on purpose to solve a particular problem. Hence logarithms were invented, but natural logarithms were discovered.
- 00:03 It is difficult to pinpoint the exact date the number e was discovered. It is suggested that it was discovered by Jacob Bernoulli in 1683 while studying a question about compound interest. However Bernoulli didn’t find the value of the number nor did he link it with the natural logarithm. It was in 1748 that Leonhard Euler found the value of e and understood that it is the base of natural logarithms. And since the natural logarithm was discovered in 1647 through the work of Gregoire de Saint Vincent and Alfonso de Sarasa, it was therefore discovered between 36 years and 101 years before the discovery of the number e.
- 2:28 Some sources credit Jost Burgi with the invention of logarithms. Although there is evidence that he did come up with a similar idea before Napier, he didn’t publish it till after the success of Napier’s logarithms. Also, Burgi's approach was different and doesn't lend itself to understanding the natural logarithm.
- 07:09 I omitted the decimal points, the correct values are 9999998.0000001, 9999997.0000003 and so on. While Napier included those decimal points when he calculated the tables, he omitted them in the final result.
- 7:09 For Napier’s logarithms to work with multiplication and division, we have to divide by 10^7.
- 7:39 Napier published two books regarding logarithms: the Descriptio which describes how to use logarithms and the Constructio, which describes how to construct them (published posthumously). Modern English translations for both books are available at: http://www.17centurymaths.com/
- 8:06 There is a lot of conflicting information about how Oughtred calculated his logarithms, “Wikipedia number e” page suggests that he calculated them from the number e, which is highly unlikely since the number e, as mentioned in the notes above, was not discovered till at least another 65 years, and even then, it’s value wasn’t calculated till yet another 65 years. A source I found most convincing is in the note below.
- 9:16 The link to how Oughtred and Speidell came up with logarithms that resemble natural logarithms https://www.tandfonline.com/doi/full/10.1080/17498430.2015.1116052
- 9:20 The way I explain it is not how Oughtred and Speidell calculated their tables, however, it gives a better understanding of what the natural logarithm is.
- 9:33 The smaller the base, the closer the result is to the natural logarithm. I chose 1.000001 to match the results of Oughtred and Speidell.
- 9:39 Again, I omitted extra decimal points, the correct values are: 1.000002000001, 1.000003000003 and so on.
-17:29 The statement: “It is not clear why Mercator called it the natural logarithm” may raise eyebrows as the following three ideas are usually given as a reason: 1. e is a quantity which arises frequently and unavoidably in nature, 2. Natural logarithms have the simplest derivatives of all the systems of logarithms and 3. In the calculation of logarithms to any base, logarithms to the base e are first calculated, then multiplied by a constant which depends on the system being calculated. See https://www.jstor.org/stable/3028204. However none of these ideas were known at Mercator’s time and there must have been a different reason as to why he called it the natural logarithm.
https://wn.com/The_History_Of_The_Natural_Logarithm_How_Was_It_Discovered
- Learning about the history of the natural logarithm helps us understand what it is.
Today we define the natural logarithm as a logarithm with the base e and many people, understandably, wonder why! Interestingly the natural logarithm was discovered decades before the number e. In fact it was discovered before the link between logarithms and exponentials was recognized!
In this video I talk about how and why logarithms were invented, how the natural logarithm arise from from logarithmic tables without the need of the number e and how studying the area of the hyperbola was instrumental in defining logarithms and the natural logarithm.
Support this channel
Your support of the channel is very much appreciated. You can do so at the links below. Thanks for keeping me going :)
- Buy me a coffee: https://www.buymeacoffee.com/tareksaid
- Support me on PayPal: http://bit.ly/3FmhvEo
- Patreon: https://www.patreon.com/tareksaid
Corrections:
- 11:33 The name of the hyperbola is: "Rectangular Hyperbola" not "Square Hyperbola"
-12:36 I realised after publishing the video that the method I used was not the method that was used by Saint Vincent. For the original method by Saint Vincent check: https://www.jstor.org/stable/3620207
-15:13 Saint Vincent didn't make the connection with the logarithms, he only discovered that they areas are equal. It was de Sarasa who made the connection
Notes:
- 00:02 I am using the terms discovered and invented in a specific sense. “Discovered” when a mathematical idea was stumbled upon, while “invented” when it was created on purpose to solve a particular problem. Hence logarithms were invented, but natural logarithms were discovered.
- 00:03 It is difficult to pinpoint the exact date the number e was discovered. It is suggested that it was discovered by Jacob Bernoulli in 1683 while studying a question about compound interest. However Bernoulli didn’t find the value of the number nor did he link it with the natural logarithm. It was in 1748 that Leonhard Euler found the value of e and understood that it is the base of natural logarithms. And since the natural logarithm was discovered in 1647 through the work of Gregoire de Saint Vincent and Alfonso de Sarasa, it was therefore discovered between 36 years and 101 years before the discovery of the number e.
- 2:28 Some sources credit Jost Burgi with the invention of logarithms. Although there is evidence that he did come up with a similar idea before Napier, he didn’t publish it till after the success of Napier’s logarithms. Also, Burgi's approach was different and doesn't lend itself to understanding the natural logarithm.
- 07:09 I omitted the decimal points, the correct values are 9999998.0000001, 9999997.0000003 and so on. While Napier included those decimal points when he calculated the tables, he omitted them in the final result.
- 7:09 For Napier’s logarithms to work with multiplication and division, we have to divide by 10^7.
- 7:39 Napier published two books regarding logarithms: the Descriptio which describes how to use logarithms and the Constructio, which describes how to construct them (published posthumously). Modern English translations for both books are available at: http://www.17centurymaths.com/
- 8:06 There is a lot of conflicting information about how Oughtred calculated his logarithms, “Wikipedia number e” page suggests that he calculated them from the number e, which is highly unlikely since the number e, as mentioned in the notes above, was not discovered till at least another 65 years, and even then, it’s value wasn’t calculated till yet another 65 years. A source I found most convincing is in the note below.
- 9:16 The link to how Oughtred and Speidell came up with logarithms that resemble natural logarithms https://www.tandfonline.com/doi/full/10.1080/17498430.2015.1116052
- 9:20 The way I explain it is not how Oughtred and Speidell calculated their tables, however, it gives a better understanding of what the natural logarithm is.
- 9:33 The smaller the base, the closer the result is to the natural logarithm. I chose 1.000001 to match the results of Oughtred and Speidell.
- 9:39 Again, I omitted extra decimal points, the correct values are: 1.000002000001, 1.000003000003 and so on.
-17:29 The statement: “It is not clear why Mercator called it the natural logarithm” may raise eyebrows as the following three ideas are usually given as a reason: 1. e is a quantity which arises frequently and unavoidably in nature, 2. Natural logarithms have the simplest derivatives of all the systems of logarithms and 3. In the calculation of logarithms to any base, logarithms to the base e are first calculated, then multiplied by a constant which depends on the system being calculated. See https://www.jstor.org/stable/3028204. However none of these ideas were known at Mercator’s time and there must have been a different reason as to why he called it the natural logarithm.
- published: 04 Mar 2022
- views: 493096
10:34
Natural Logarithms
Find a local tutor in you area now! Get homework help now! FREE online Tutoring on Thursday nights! All FREE @ http://textbooktactics.com
Click show more for V...
Find a local tutor in you area now! Get homework help now! FREE online Tutoring on Thursday nights! All FREE @ http://textbooktactics.com
Click show more for Video Description:
Natural Logarithms: Introduction to natural logarithms, using log properties to simplify or expand natural logarithms, solving natural logarithms, and using natural logarithms to solve exponential equations with a natural base e.
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https://wn.com/Natural_Logarithms
Find a local tutor in you area now! Get homework help now! FREE online Tutoring on Thursday nights! All FREE @ http://textbooktactics.com
Click show more for Video Description:
Natural Logarithms: Introduction to natural logarithms, using log properties to simplify or expand natural logarithms, solving natural logarithms, and using natural logarithms to solve exponential equations with a natural base e.
If you enjoy this video, Please follow us on YouTube, Facebook and Twitter!
Check out our Website for more Video's
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- published: 24 May 2012
- views: 241498
0:56
Defining the natural logarithm
The definition of the natural log as an area accumulation function. #shorts #math #manim #logarithms #calculus #integral
The definition of the natural log as an area accumulation function. #shorts #math #manim #logarithms #calculus #integral
https://wn.com/Defining_The_Natural_Logarithm
The definition of the natural log as an area accumulation function. #shorts #math #manim #logarithms #calculus #integral
- published: 25 Apr 2023
- views: 177260
1:14:54
What makes the natural log "natural"? | Ep. 7 Lockdown live math
All about ln(x).
Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev
Home page: https://www.3blue1brown.com
Brought to you b...
All about ln(x).
Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev
Home page: https://www.3blue1brown.com
Brought to you by you: https://3b1b.co/ldm-thanks
Beautiful pictorial summary by @ThuyNganVu:
https://twitter.com/ThuyNganVu/status/1259288683489849344
Errors:
At minute 16, the sum should be written with a "..." to indicate going to infinity.
At minute 38, the exponent should have 1/(2s^2) instead of 1/s^2 for s to represent standard deviation.
At minute 54, an equal sign was mistakenly used in taking the derivative of x^3 / 3!.
At the end, it should be pointed out that the alternating series with x^n terms only converges for values of x between -1 and 1, so the values one can't be considered proven with values of x outside that range. Everything with the argument here is fine, as it only deals with the convergent input, but that fact should still be mentioned.
Related videos.
Calculus series:
https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr
The sum giving pi^2 / 6:
https://youtu.be/d-o3eB9sfls
The sum giving pi / 4:
https://youtu.be/NaL_Cb42WyY
https://youtu.be/00w8gu2aL-w (Mathologer)
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
-------------------
Video timeline (thanks to user "noonesperfect")
0:00:14 - Question 1
0:02:29 - Answer 1
0:06:27 - Prime nos. in Infinite Geometric Series (Basel problem) and their relationship with Natural logarithm
0:12:01 - More examples of prime numbers in infinite series and their relationship with ln
0:17:25 - Question 2
0:19:20 - Answer 2 and explanation using ln
0:22:25 - Question 3 and families of curves
0:26:37 - Answer 3 and explanation
0:28:50 - Imaginary exponential
0:30:57 - Derivatives of exponential terms
0:37:21 - Why derivative of e^t is the same as that e^t itself?
0:41:21 - Question 4
0:44:12 - Answer 4 and explanation using Python
0:46:02 - Taylor Series for e^x
0:48:29 - Derivatives of polynomial terms/Derivatives of e^x
0:50:56 - Derivative of natural logarithm using graph
0:56:07 - Question 5
0:57:37 - Answer 5 and explanation
1:02:15 - Euler–Mascheroni constant
1:08:37 - Question 6
1:12:41 - Connecting dots to the familiarity of different expression in math
------------------
The live question setup with stats on-screen is powered by Itempool.
https://itempool.com/
Curious about other animations?
https://www.3blue1brown.com/faq#manim
Music by Vincent Rubinetti.
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
https://wn.com/What_Makes_The_Natural_Log_Natural_|_Ep._7_Lockdown_Live_Math
All about ln(x).
Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev
Home page: https://www.3blue1brown.com
Brought to you by you: https://3b1b.co/ldm-thanks
Beautiful pictorial summary by @ThuyNganVu:
https://twitter.com/ThuyNganVu/status/1259288683489849344
Errors:
At minute 16, the sum should be written with a "..." to indicate going to infinity.
At minute 38, the exponent should have 1/(2s^2) instead of 1/s^2 for s to represent standard deviation.
At minute 54, an equal sign was mistakenly used in taking the derivative of x^3 / 3!.
At the end, it should be pointed out that the alternating series with x^n terms only converges for values of x between -1 and 1, so the values one can't be considered proven with values of x outside that range. Everything with the argument here is fine, as it only deals with the convergent input, but that fact should still be mentioned.
Related videos.
Calculus series:
https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr
The sum giving pi^2 / 6:
https://youtu.be/d-o3eB9sfls
The sum giving pi / 4:
https://youtu.be/NaL_Cb42WyY
https://youtu.be/00w8gu2aL-w (Mathologer)
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
-------------------
Video timeline (thanks to user "noonesperfect")
0:00:14 - Question 1
0:02:29 - Answer 1
0:06:27 - Prime nos. in Infinite Geometric Series (Basel problem) and their relationship with Natural logarithm
0:12:01 - More examples of prime numbers in infinite series and their relationship with ln
0:17:25 - Question 2
0:19:20 - Answer 2 and explanation using ln
0:22:25 - Question 3 and families of curves
0:26:37 - Answer 3 and explanation
0:28:50 - Imaginary exponential
0:30:57 - Derivatives of exponential terms
0:37:21 - Why derivative of e^t is the same as that e^t itself?
0:41:21 - Question 4
0:44:12 - Answer 4 and explanation using Python
0:46:02 - Taylor Series for e^x
0:48:29 - Derivatives of polynomial terms/Derivatives of e^x
0:50:56 - Derivative of natural logarithm using graph
0:56:07 - Question 5
0:57:37 - Answer 5 and explanation
1:02:15 - Euler–Mascheroni constant
1:08:37 - Question 6
1:12:41 - Connecting dots to the familiarity of different expression in math
------------------
The live question setup with stats on-screen is powered by Itempool.
https://itempool.com/
Curious about other animations?
https://www.3blue1brown.com/faq#manim
Music by Vincent Rubinetti.
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
- published: 08 May 2020
- views: 1520810
10:16
The Exponential Function e and The Natural Log ln
A Level Maths revision tutorial video.
For the full list of videos and more revision resources visit www.mathsgenie.co.uk.
A Level Maths revision tutorial video.
For the full list of videos and more revision resources visit www.mathsgenie.co.uk.
https://wn.com/The_Exponential_Function_E_And_The_Natural_Log_Ln
A Level Maths revision tutorial video.
For the full list of videos and more revision resources visit www.mathsgenie.co.uk.
- published: 12 Sep 2017
- views: 271278
3:15
9012 48 Ave NW, Calgary | Idyllic Log Home on 0.55 Acres
Welcome to your private log home retreat, nestled along the river next to Bowness Park—a sanctuary where history and nature harmoniously converge. This captivat...
Welcome to your private log home retreat, nestled along the river next to Bowness Park—a sanctuary where history and nature harmoniously converge. This captivating residence showcases hand-hewn Norwegian-style logs that have aged beautifully, providing natural insulation for cozy winters and cool summers.
Approaching the home, you are greeted by an inviting front porch—perfect for morning coffees or relaxing evenings—a charming introduction to this special abode. Situated on a 50’x482’, 0.55-acre lot, the property ensures complete privacy amidst a forested landscape teeming with wildlife and a serene creek in the backyard.
Step inside to discover a captivating interior. The sunken living room boasts 25-foot open-beam cathedral ceilings and a high-efficiency MORSO stove, offering a cozy retreat. Adjacent spaces include a dining room, office area, and a half bath. The chef’s kitchen features maple cabinets, granite countertops, and large sliding doors that seamlessly blend indoor and outdoor living.
The completely secluded back deck is an entertainer’s dream, featuring elegant Italian tile flooring and a wood-fired pizza oven. The outdoor kitchen is equipped with a built-in gas BBQ and concrete countertops, perfect for culinary adventures. A timber-framed gazebo adds charm and functionality, offering a bespoke wooden table and seating benches, ideal for hosting gatherings in style.
Upstairs, a grand wood staircase leads to a beautifully renovated upper level with a flex space. The master suite is a bright sanctuary overlooking the forest with a gas fireplace and an spacious ensuite. Three additional bedrooms and a second bathroom, featuring sunroom-style windows that allow natural light to filter through the trees, complete this floor, creating a private and serene atmosphere.
Attention to detail is evident throughout with solid-core doors, soundproof bedroom walls, and sustainable beetle pine ceiling paneling. The home was designed as a forever home with meticulous updates, including a new roof and spray foam insulation for enhanced energy efficiency. The double attached garage provides ample space for vehicles and additional storage, enhancing both convenience and functionality. The partial basement features a cedar sauna and storage, and offers potential for further customization.
More than just a home, this property offers a lifestyle—a perfect blend of rustic charm and modern comforts. With its rich history, stunning surroundings, and thoughtful updates, this home embodies a rare opportunity in the heart of Bowness. Embrace a tranquil yet vibrant lifestyle, with easy access to Bowness Park’s natural beauty and recreational opportunities.
Calley Erickson Team
Sotheby’s International Realty Canada
📞 587-355-2153
📥
[email protected]
https://wn.com/9012_48_Ave_Nw,_Calgary_|_Idyllic_Log_Home_On_0.55_Acres
Welcome to your private log home retreat, nestled along the river next to Bowness Park—a sanctuary where history and nature harmoniously converge. This captivating residence showcases hand-hewn Norwegian-style logs that have aged beautifully, providing natural insulation for cozy winters and cool summers.
Approaching the home, you are greeted by an inviting front porch—perfect for morning coffees or relaxing evenings—a charming introduction to this special abode. Situated on a 50’x482’, 0.55-acre lot, the property ensures complete privacy amidst a forested landscape teeming with wildlife and a serene creek in the backyard.
Step inside to discover a captivating interior. The sunken living room boasts 25-foot open-beam cathedral ceilings and a high-efficiency MORSO stove, offering a cozy retreat. Adjacent spaces include a dining room, office area, and a half bath. The chef’s kitchen features maple cabinets, granite countertops, and large sliding doors that seamlessly blend indoor and outdoor living.
The completely secluded back deck is an entertainer’s dream, featuring elegant Italian tile flooring and a wood-fired pizza oven. The outdoor kitchen is equipped with a built-in gas BBQ and concrete countertops, perfect for culinary adventures. A timber-framed gazebo adds charm and functionality, offering a bespoke wooden table and seating benches, ideal for hosting gatherings in style.
Upstairs, a grand wood staircase leads to a beautifully renovated upper level with a flex space. The master suite is a bright sanctuary overlooking the forest with a gas fireplace and an spacious ensuite. Three additional bedrooms and a second bathroom, featuring sunroom-style windows that allow natural light to filter through the trees, complete this floor, creating a private and serene atmosphere.
Attention to detail is evident throughout with solid-core doors, soundproof bedroom walls, and sustainable beetle pine ceiling paneling. The home was designed as a forever home with meticulous updates, including a new roof and spray foam insulation for enhanced energy efficiency. The double attached garage provides ample space for vehicles and additional storage, enhancing both convenience and functionality. The partial basement features a cedar sauna and storage, and offers potential for further customization.
More than just a home, this property offers a lifestyle—a perfect blend of rustic charm and modern comforts. With its rich history, stunning surroundings, and thoughtful updates, this home embodies a rare opportunity in the heart of Bowness. Embrace a tranquil yet vibrant lifestyle, with easy access to Bowness Park’s natural beauty and recreational opportunities.
Calley Erickson Team
Sotheby’s International Realty Canada
📞 587-355-2153
📥
[email protected]
- published: 29 Jun 2024
- views: 66
19:15
Logarithms... How? (NancyPi)
MIT grad introduces logs and shows how to evaluate them. To skip ahead: 1) For how to understand and evaluate BASIC LOGS, skip to time 0:52. 2) For how to evalu...
MIT grad introduces logs and shows how to evaluate them. To skip ahead: 1) For how to understand and evaluate BASIC LOGS, skip to time 0:52. 2) For how to evaluate weirder logs, including the log of 0, 1, a FRACTION, or a NEGATIVE number, skip to time 6:44. 3) For NATURAL LOGS (LN X), skip to time 11:17. 4) For even weirder logs, including SOLVING for X and using the CHANGE-OF-BASE formula, skip to time 14:56. Nancy formerly of MathBFF explains the steps.
Follow Nancy on Instagram: https://instagram.com/nancypi
Twitter: https://twitter.com/nancypi
1) BASIC LOGS: you can read log notation as "log, base 3, of 9 equals X". The small (subscript) number is called the base. You can always evaluate a log expression by rearranging it into something called exponential form. Every log expression is connected to an exponential expression. In this example, the log is connected to the exponential form "3 to the X power equals 9". This means, "3 raised to what power gives you 9?" Since 3 raised to the power of 2 equals 9, the answer for X is 2. This is also the answer for the value of the log expression. The log is always equal to the power (or exponent) in the exponential version, and in this case it equals 2. If you want, you can find the log value in your head just by asking yourself what power you need in order to turn the base number into the middle number ("argument" number). Note: if there is no base number in the log expression (no little subscript number), then the base is 10, since 10 is the default base.
2) WEIRDER LOGS (log of 0, 1, a negative number, or a fraction): you can use the same steps to rearrange log expressions that have a fraction, negative number, 0, or 1 in them. You can still rearrange them to be in exponential form just like you can with the basic logs from earlier. The log of 1 will always be 0, since 0 is the only power that can turn a base into 1. The log of 0 will always be undefined, since no power can turn a base into 0. The log of a negative number is undefined in the real number system, since no real power can turn a positive base into a negative number.
3) NATURAL LOGS (ln x): the natural log is just a special type of log where the base is e (the special math constant e, which is approximately 2.718 if you plug it into your calculator). You can use the same steps for rearranging the log expression into exponential form. Just remember that ln x means log, base e.
4) EVEN WEIRDER LOGS (solving for X, change-of-base formula): even if there is an X variable in the log part of an equation, you can still rearrange the equation into exponential form. This will let you solve for X. Sometimes you might need to use the change-of-base formula to evaluate a log expression. If there is no whole number power you know that works, it may actually be a decimal power that you can find by using the change-of-base formula. For example, you can re-write log, base 2, of 7 as (log 7)/(log 2) and use your calculator to find the decimal number if you need it.
For more of my math videos, check out: http://nancypi.com
https://wn.com/Logarithms..._How_(Nancypi)
MIT grad introduces logs and shows how to evaluate them. To skip ahead: 1) For how to understand and evaluate BASIC LOGS, skip to time 0:52. 2) For how to evaluate weirder logs, including the log of 0, 1, a FRACTION, or a NEGATIVE number, skip to time 6:44. 3) For NATURAL LOGS (LN X), skip to time 11:17. 4) For even weirder logs, including SOLVING for X and using the CHANGE-OF-BASE formula, skip to time 14:56. Nancy formerly of MathBFF explains the steps.
Follow Nancy on Instagram: https://instagram.com/nancypi
Twitter: https://twitter.com/nancypi
1) BASIC LOGS: you can read log notation as "log, base 3, of 9 equals X". The small (subscript) number is called the base. You can always evaluate a log expression by rearranging it into something called exponential form. Every log expression is connected to an exponential expression. In this example, the log is connected to the exponential form "3 to the X power equals 9". This means, "3 raised to what power gives you 9?" Since 3 raised to the power of 2 equals 9, the answer for X is 2. This is also the answer for the value of the log expression. The log is always equal to the power (or exponent) in the exponential version, and in this case it equals 2. If you want, you can find the log value in your head just by asking yourself what power you need in order to turn the base number into the middle number ("argument" number). Note: if there is no base number in the log expression (no little subscript number), then the base is 10, since 10 is the default base.
2) WEIRDER LOGS (log of 0, 1, a negative number, or a fraction): you can use the same steps to rearrange log expressions that have a fraction, negative number, 0, or 1 in them. You can still rearrange them to be in exponential form just like you can with the basic logs from earlier. The log of 1 will always be 0, since 0 is the only power that can turn a base into 1. The log of 0 will always be undefined, since no power can turn a base into 0. The log of a negative number is undefined in the real number system, since no real power can turn a positive base into a negative number.
3) NATURAL LOGS (ln x): the natural log is just a special type of log where the base is e (the special math constant e, which is approximately 2.718 if you plug it into your calculator). You can use the same steps for rearranging the log expression into exponential form. Just remember that ln x means log, base e.
4) EVEN WEIRDER LOGS (solving for X, change-of-base formula): even if there is an X variable in the log part of an equation, you can still rearrange the equation into exponential form. This will let you solve for X. Sometimes you might need to use the change-of-base formula to evaluate a log expression. If there is no whole number power you know that works, it may actually be a decimal power that you can find by using the change-of-base formula. For example, you can re-write log, base 2, of 7 as (log 7)/(log 2) and use your calculator to find the decimal number if you need it.
For more of my math videos, check out: http://nancypi.com
- published: 19 Aug 2018
- views: 3377156