Most simply put, logarithms are inverses of exponentials.
Check it out:
Let's graph the inverse of
Remember that every ( x , y ) has a ( y , x ) partner, so we'll graph this guy... then nail his inverse!
This is the inverse of
Remember the steps to find the inverse of a function using algebra? In one part, you switch the x and the y -- right?
So, we COULD say that the inverse of
But... ya know... in math, we really like to write things like