What the hell are logarithms? I can explain that. Somewhat.

First, logarithms are written in the following form:

log^a_b

In this form, 'a' represents the number you are 'logging' and 'b' represents the base that you are using. A logarithm means: To what power to I( have to raise 'b' in order to get 'a'?

Example:

log^1,000,000₁₀

This means "To what power do I have to raise 10 in order to get 1,000,000?". The answer is 6 (10⁶=1,000,000), so 'log 1,000,000 with a base of 10' is 6.

You can use any base you want. (If you do not see a base number, you assume the base is 10). For example:

A natural log is simply a logarithm with a base of 'e', a number that is imporant in calculus for some ridiculously complicated reason. 'e' is approximately equal to 2.71828. (it is a decimal that goes on and on forever, much like pi)

log^x_2.71828

X is whatever number you want to take a natural log of. Natural logs are abbreviated LN.

Since logariths are exponent-based functions, that means that as the number you are logging gets higher and higher, your result increases by smaller and smaller increments.