The logarithm of a number is the power to which the base must be raised to get the number.

The logarithm of a number is the power to which the base must be raised to get the number. Although the full name is 'logarithm', people often just say 'log' instead. The base can be any real number, but two values are most typical. When the base is $10$, we say we are using the 'common log'. On the other hand, when the base is $e$ ($\approx 2.718281828$), we say we are using the 'natural log'. The natural log can be mathematically convenient, whereas the common log is more intuitive for many people because every increment is $10\times$ greater than the previous value.