First let's start off with what elementary algebra: it is fancy counting. Logarithms are just a continuation of this but in a slightly advanced way.
The definition of a logarithm is the inverse of an exponential, in other words: something to the power of x. Whilst, the same can be said for an exponential. An exponential is just the inverse of a logarithm.
Logarithms are used when you know what you are counting to, and you know what step you want to take. But you don't know how many steps to take.
For example. To get to 81, using steps of x9 you need 2 steps.
But say you don't know that, what would you do?
Well, in a system that counts in a times nine sort of way, 81 is equal to two steps.
STC = Sytem that counts
That can be rewritten as
STC x 9 81 = 2
In a system that counts in a times 9 sort of way to the integer 81, it takes two steps.
Now, we just write "STC" as "LOG" for logarithm.
Log9(81) = 2
When answering this question with a calculator, it can be done by dividing log81 by log9
Log81/log9 = 2
Log follows exponential rules where
X^x = x^x * x^x
X^7 = x^3 * x^4
Log9(81) = Log81 / Log9
Except you change the normal multiplication to division.
Remember, the log of something is any old number. It is nothing special, just a special way to get to it.