I would like to know where are the excersices used in this video located so I can practice the forwards and backwards conversion :)

This https://www.khanacademy.org/math/algebra2/logarithms-tutorial/logarithm_basics/e/understanding-logs-as-inverse-exponentials

Who came up with the idea of logarithms?

The modern logarithm was developed by several people, but John Napier is often credited as being the most influential. He published a book in 1614 that contained (amongst other concepts) the beginnings of the modern logarithm. There have been a few improvements to the concept since his time.

What exactly is the point of logarithms?? Why don't we just use exponents??

When you move on to more advanced math, you will see why. There are functions which need to be expressed using logarithms and cannot be expressed with exponents. Logarithms are one of the most useful functions in real world, applied mathematics.

How do you use logarithm for richter scale?

The Richter scale rating of an earthquake is the base 10 logarithm of the ratio of the intensity of the earthquake to the intensity of a barely detectable earthquake. For example, an earthquake that is 100,000 times as intense as a barely detectable earthquake has a Richter scale rating of log base 10 of 100,000, which equals 5 (because 10^5=100,000). This logarithmic relationship implies that each time the Richter scale rating increases by 1 point, the intensity is multiplied by 10. For example, a Richter scale 6 earthquake is 10 times as intense as a Richter scale 5 earthquake; a Richter scale 5 earthquake is 10*10=10^2=100 times as intense as a Richter scale 3 earthquake.

At 0:33, wouldn't log_10(100) just be log(100) since 10 is the common log base?

I have no idea if this question would have accepted log(100), this is an old video and khan academy doesn't use that layout anymore.

Has Sal ever gotten a question wrong?

Everyone makes mistakes, even Sal. You will sometimes see a correction box pop up on a video to correct a mistake made in the video.

In the video @ 1:25 Sy's answer is 5^(-3) = 1/125 Would it be wrong to answer 1/125 = 5^(-3)?

No, it wouldn't be incorrect. As both sides are equal, they can be switched either way, as long as each side is still equal. :P

Is logarithms even used in real life? Is it useful?

There's actually extremely useful examples for using logarithms: - Portraying large numbers in a graph (notice most COVID-19 case graphs has a logarithmic scale) - Many natural phenomena works in logarithms such as cooling and heating down substances - pH, pH3O & pOH - Richter Scale There's many more uses than this ! If someone else answers you I'm sure you will be able to find more examples (or you can search it up)

Main content

Integrated math 3

Course: Integrated math 3 > Unit 5

Lesson 1: Introduction to logarithms

Relationship between exponentials & logarithms

Name: Relationship between exponentials & logarithms
Uploaded: 2014-03-28T15:01:28Z
Description: Sal rewrites 100=10^2 as a logarithmic equation and log_5(1/125)=-3 as an exponential equation.

Google Classroom

Sal rewrites 100=10^2 as a logarithmic equation and log_5(1/125)=-3 as an exponential equation. Created by Sal Khan.

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Ricardo Marques
Posted 10 years ago. Direct link to Ricardo Marques's post “I would like to know wher...”
I would like to know where are the excersices used in this video located so I can practice the forwards and backwards conversion :)
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(69 votes)
Answer
- Saheel Wagh
  Posted 10 years ago. Direct link to Saheel Wagh's post “This https://www.khanacad...”
  This https://www.khanacademy.org/math/algebra2/logarithms-tutorial/logarithm_basics/e/understanding-logs-as-inverse-exponentials
  Comment on Saheel Wagh's post “This https://www.khanacad...”
  (53 votes)
Beans
Posted 8 years ago. Direct link to Beans's post “Who came up with the idea...”
Who came up with the idea of logarithms?
Button navigates to signup pageComment on Beans's post “Who came up with the idea...”
(28 votes)
Answer
- Just Keith
  Posted 8 years ago. Direct link to Just Keith's post “The modern logarithm was ...”
  The modern logarithm was developed by several people, but John Napier is often credited as being the most influential. He published a book in 1614 that contained (amongst other concepts) the beginnings of the modern logarithm. There have been a few improvements to the concept since his time.
  Button navigates to signup page
  (26 votes)
RISHI
Posted 8 years ago. Direct link to RISHI's post “What exactly is the point...”
What exactly is the point of logarithms?? Why don't we just use exponents??
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(17 votes)
Answer
- Just Keith
  Posted 8 years ago. Direct link to Just Keith's post “When you move on to more ...”
  When you move on to more advanced math, you will see why. There are functions which need to be expressed using logarithms and cannot be expressed with exponents.
  
  Logarithms are one of the most useful functions in real world, applied mathematics.
  Comment on Just Keith's post “When you move on to more ...”
  (21 votes)
FERDOUS SIDDIQUE
Posted 4 years ago. Direct link to FERDOUS SIDDIQUE's post “How do you use logarithm ...”
How do you use logarithm for richter scale?
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(6 votes)
Answer
- Ian Pulizzotto
  Posted 4 years ago. Direct link to Ian Pulizzotto's post “The Richter scale rating ...”
  The Richter scale rating of an earthquake is the base 10 logarithm of the ratio of the intensity of the earthquake to the intensity of a barely detectable earthquake. For example, an earthquake that is 100,000 times as intense as a barely detectable earthquake has a Richter scale rating of log base 10 of 100,000, which equals 5 (because 10^5=100,000).
  
  This logarithmic relationship implies that each time the Richter scale rating increases by 1 point, the intensity is multiplied by 10. For example, a Richter scale 6 earthquake is 10 times as intense as a Richter scale 5 earthquake; a Richter scale 5 earthquake is 10*10=10^2=100 times as intense as a Richter scale 3 earthquake.
  Comment on Ian Pulizzotto's post “The Richter scale rating ...”
  (12 votes)
The 6th Epic Nerd
Posted 8 years ago. Direct link to The 6th Epic Nerd's post “In the video @ 1:25 Sy's ...”
In the video @
1:25
Sy's answer is 5^(-3) = 1/125
Would it be wrong to answer 1/125 = 5^(-3)?
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(3 votes)
Answer
- Kitty Ashleigh
  Posted 8 years ago. Direct link to Kitty Ashleigh's post “No, it wouldn't be incorr...”
  No, it wouldn't be incorrect. As both sides are equal, they can be switched either way, as long as each side is still equal. :P
  Comment on Kitty Ashleigh's post “No, it wouldn't be incorr...”
  (11 votes)
Anant Singh
Posted 3 years ago. Direct link to Anant Singh's post “Is logarithms even used i...”
Is logarithms even used in real life? Is it useful?
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(3 votes)
Answer
- A/V
  Posted 3 years ago. Direct link to A/V's post “There's actually extremel...”
  There's actually extremely useful examples for using logarithms:
  - Portraying large numbers in a graph (notice most COVID-19 case graphs has a logarithmic scale)
  - Many natural phenomena works in logarithms such as cooling and heating down substances
  - pH, pH3O & pOH
  - Richter Scale
  
  There's many more uses than this ! If someone else answers you I'm sure you will be able to find more examples (or you can search it up)
  Button navigates to signup page
  (9 votes)
Siqueiros Crystal
Posted 10 months ago. Direct link to Siqueiros Crystal's post “Rewrite the following equ...”
Rewrite the following equation in logarithmic form.
16=8 4/3
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(4 votes)
Answer
- David Severin
  Posted 10 months ago. Direct link to David Severin's post “It would be log(base 8) 1...”
  It would be log(base 8) 16 = 4/3. the base 8 is written as 8 subscripted.
  Button navigates to signup page
  (7 votes)
Ann
Posted 3 years ago. Direct link to Ann's post “At 0:33, wouldn't log_10(...”
At
0:33
, wouldn't log_10(100) just be log(100) since 10 is the common log base?
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(6 votes)
Answer
- loumast17
  Posted 3 years ago. Direct link to loumast17's post “I have no idea if this qu...”
  I have no idea if this question would have accepted log(100), this is an old video and khan academy doesn't use that layout anymore.
  Button navigates to signup page
  (3 votes)
GhostOfNoch
Posted 2 years ago. Direct link to GhostOfNoch's post “Has Sal ever gotten a que...”
Has Sal ever gotten a question wrong?
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(5 votes)
Answer
- Kim Seidel
  Posted 2 years ago. Direct link to Kim Seidel's post “Everyone makes mistakes, ...”
  Everyone makes mistakes, even Sal. You will sometimes see a correction box pop up on a video to correct a mistake made in the video.
  Button navigates to signup page
  (4 votes)
jazzybenigno11
Posted 8 years ago. Direct link to jazzybenigno11's post “How would you change an e...”
How would you change an equation to exponential form if there were two logarithims in the equation?
a
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(5 votes)
Answer

Video transcript

Voiceover:Rewrite the following equation in logarithmic form. So they wrote 100 is equal to 10 to the second power. So if we wanna write the same information, really, in logarithmic form, we could say that the power that I need to raise 10 to to get to 100 is equal to 2, or log base 10 of 100 is equal to 2. Notice these are equivalent statements. This is just in exponential form. This is is logarithmic form. This is saying that the power I need to raise 10 to to get to 100 is equal to 2. Which is the same thing as saying that 10 to the 2nd power is 100. 10 to the second power is 100. And the way that I specify the base is by doing this underscore right over here. So underscore 10, log base 10 of 100 is equal to 2. Here they ask us to rewrite the following equation in exponential form. So this is log base 5 of 1 over 125 is equal to negative 3. This is one way to think about it is saying the power that I need to raise 5 to to get to 1 over 125 is equal to negative 3 or that 5 to the negative 3 power is equal to 1 over 125. And we can verify that this has formatted it the right way. 5 to the negative 3 power is 1 over 125. The exact same truth about the universe, just in different forms. Logarithmic form and exponential form. So let me check my answer and make sure I got it right. And I did.