Logarithms are a way of expressing powers.

The logarithm log_b{x} for a base b and a number x is defined to be the inverse function of taking b to the power x, i.e., b^x.¹

The simplest way to explain the concept of logarithms is through an example:

tabular{000}{0000}{{2^5} = {32} {log_2{32}} = 5}

The subscript of the logarithm above denotes the base of the logarithm. This is equivalent to the number which is raised to a power in the preceding equation. The logarithm to the base 2 of 32 is 5, because 2 to the power of 5 is 32.

x^y = z doubleleftright log_x z = y

¹ Weisstein, Eric W. “Logarithm.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/Logarithm.html