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## Algebra 2 (Eureka Math/EngageNY)

### Course: Algebra 2 (Eureka Math/EngageNY)>Unit 3

Lesson 9: Topic C: Lessons 17-22: Graphs of exponential and logarithmic functions

# 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 :)
• 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.
• In the video @ 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)
• At , 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.
• How would you change an equation to exponential form if there were two logarithims in the equation?
a