Unlike the two most “friendly” arithmetic operations, addition and multiplication, exponentiation is not commutative. You will get a **different** result if you swap the value in the base with the one in the exponent (unless, of course, they are the same value):

The most significant impact of this lack of commutativity arises when you need to solve an equation that involves exponentiation: two different inverse functions are needed, one to undo the exponent (a root), and a different one to undo the base (a logarithm).

Just as there are many versions of the addition function (adding 2, adding 5, adding 7.23, etc.), and many versions of the “root” function (square roots, cube roots, etc.), there are also many versions of the “logarithm” function. Each version has a “base”, which corresponds to the base of its inverse exponential expression.

### Inverse Functions: Logarithms & Exponentials

Logarithms are labelled with a number that corresponds to the base of the exponential that they undo. For example, the Continue reading Logarithms