What is the relationship between logarithms and radicals?

Here's my question: what is the relationship between radicals and logarithms? How are they related?

(My original question is below, but the answer occurred to me after I posted it)

I have a simple question--why is the inverse of an exponential function a logarithmic function instead of a radical function?

If $\displaystyle F(x) = 5^x$, wouldn't the inverse be $\displaystyle x = 5^y$, and couldn't that be written $\displaystyle \sqrt[5]{x}$? Why must it be written $\displaystyle log_5x$