Definition of Base - Logarithm Base

The base of a logarithm is b in the following notation:

This is the classic layout of a logarithm. It is read "the log, base b of a, is x". The laymen's meaning of the equation is what power must one raise b to in order to achieve a? or simply,

Usually, there are only two bases ever used in everyday applications, base 10, which is referred to as the common logarithm, and base e, or the natural logarithm. e= 2.71828.

Logarithms in base 10 are usually just written as log x, while base e logarithms are usually just written as ln x.