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## Algebra (all content)

### Course: Algebra (all content)ย >ย Unit 11

Lesson 22: Introduction to logarithms (Algebra 2 level)- Intro to logarithms
- Intro to Logarithms
- Evaluate logarithms
- Evaluating logarithms (advanced)
- Evaluate logarithms (advanced)
- Relationship between exponentials & logarithms
- Relationship between exponentials & logarithms: graphs
- Relationship between exponentials & logarithms: tables
- Relationship between exponentials & logarithms

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# Relationship between exponentials & logarithms

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

## Want to join the conversation?

- I would like to know where are the excersices used in this video located so I can practice the forwards and backwards conversion :)(69 votes)
- Who came up with the idea of logarithms?(27 votes)
- 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.(25 votes)

- What exactly is the point of logarithms?? Why don't we just use exponents??(16 votes)
- 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.(20 votes)

- How do you use logarithm for richter scale?(5 votes)
- 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.(11 votes)

- In the video @1:25Sy's answer is 5^(-3) = 1/125

Would it be wrong to answer 1/125 = 5^(-3)?(2 votes)- 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(10 votes)

- Is logarithms even used in real life? Is it useful?(3 votes)
- 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)(7 votes)

- At0:33, wouldn't log_10(100) just be log(100) since 10 is the common log base?(5 votes)
- 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.(3 votes)

- How would you change an equation to exponential form if there were two logarithims in the equation?

a(4 votes) - Does anyone have an easy way to remember which component goes where?(3 votes)
- I just have a formula: y=bหx is the same as x=log (base b) y

Hope this helps!(4 votes)

- what is the formula for a logarithm(3 votes)
- A logarithm is an operation, just like addition or subtraction, so there isn't really any one formula to evaluate what a logarithm is (unless you could other ways to write a logarithm, such as an infinite series of polynomials in a Taylor series). A logarithm just basically asks "What exponent do I have to raise my base to to get this value?" It is the inverse operation of raising something to a power. Just like you can multiply something by a number and divide it by the same number to get the original number back, you can raise a number to a power and then take the log with the same base and get the power back.(3 votes)

## 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.