How is logarithmic functions as inverses of exponential?

Answer 1

An inverse of a function is found by swapping the x and y variables. For example: the straight line function y = 2x, has an inverse of x = 2y. This can be rearranged into y = x/2.

Now take the function y = ex. The inverse is: x = ey. Unfortunately, there is no easy way to rearrange this to be y = {something}. So the logarithm function was created to handle this, and now the function {x = ey} can be written as y = ln(x).