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Question:
What is the intuition behind/mathematical purpose of using logarithms and natural logs? I know the definition and the algebraic rules of manipulting them, I just never got the why of using them.



Replies:
Logs help you answer the question "four to what power equals seven". What if you were doing an experiment and you got the following data:

x y
1 1
2 4
3 9
4 16

You'd say "Oh, I get it. I bet if I set x to 5 I'd get 25." But you'll probably never do a real experiment and get data with a pattern so easy to recognize. You might get something like the following:

x y
1 1.00
2 4.92
3 12.5
4 24.3

At this point you could say "Seems like there's something simple going on, but I don't quite get it.", or you could take ln(y)/ln(x) and get it immediately.

Logs are good for making certain kinds of things easier to understand, and for making certain kinds of problems easier to solve. They're just another tool.

Tim



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