TITLE: What's the inverse operation of exponents?
QUESTION [48 upvotes]: You know, like addition is the inverse operation of subtraction, vice versa, multiplication is the inverse of division, vice versa , square is the inverse of square root, vice versa.
What's the inverse operation of exponents (exponents: 3^5)

REPLY [18 votes]: There are two inverse operations of exponentiation.
Logarithm
$$
    \log _{b} a
$$
It's read "base-$b$ logarithm of $a$".
And it means "the exponent which $b$ must be raised to, so that the result is $a$".
Root
$$
 \sqrt[b] a
$$
It's read "$b$-th root of $a$". And it means "the number which, when raised to $b$, produces $a$".