For the usual y = f(x), the input is x and the output is y.
For the INVERSE function x = f^-1(y), the input is y and the output is x.

If y equals x cubed, then x is the cube root of y : that is the inverse.

If y is the great function e^x, then x is the NATURAL LOGARITHM ln y.

Start at y, go to x = ln y, then back to y = e^(ln y).
So the LOGARITHM is the EXPONENT that produces y.  
The logarithm of y = e^5 is ln y = 5.    Logarithms grow very slowly…….

Professor Strang’s Calculus textbook (1st edition, 1991) is freely available here.

Subtitles are provided through the generous assistance of Jimmy Ren.