The common logarithm is the logarithm to base 10. The notation
is used by physicists, engineers, and calculator keypads to denote the common logarithm.
However, mathematicians generally use the same symbol to mean the natural
logarithmln, . Worse still, in Russian literature the notation is used to denote a base-10 logarithm, which conflicts with
the use of the symbol lg to indicate the logarithm to base
2. To avoid all ambiguity, it is best to explicitly specify when the logarithm to base 10 is intended. In this
work, ,
is used for the natural
logarithm, and
is used for the logarithm to the base 2.

The situation is complicated even more by the fact that number theorists (e.g., Ivić 2003) commonly use the notation to denote the nested
natural logarithm .