I am trying to gain a more intuitive feeling for the use of logarithms.
So, my questions: What do you use them for? Why were they invented? What are typical situations where one should think: "hey, let's take the $\log$!"?
Thanks for the great comments!
Here a short summary what we have so far:
Logarithms were first published 1614 by John Napier (mathematician/astronomer) . He needed them for simplifying the multiplication of large numbers.
- In regression analysis: If you expect a predictor variable to follow a power/exponential law, take the corresponding logarithm to linearize the relationship.
- In finance to calculate compound interests.
- Or more general: to calculate the time variable in growth/decay functions. (Nuclear decay, biological growth…)
- In computer science to avoid underflow. (Cool trick! But seriously: 32-bit? Take a double ;-)
- In the Prime Number Theorem
- For handling very large/small numbers (pH, etc.)
- Plotting (if your scale gets too large)