Help me!!

a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.

Here is an example   (base 10 )

47=10^1.67209

So the log of 47   is  1.67209

how can I shorten the definition for the logarithm?

A logarithm is a way to show the exponent for a base that equals a number.

For example, \((log_28=3) = (2^3=8)\) 

The little number under the log is the base of the exponent.

The number next to the little number is the answer to the exponent.

The answer of log is the exponent.

I can draw pictures of it later if you still need assistance.