# Logarithm

From AMS Glossary

## logarithm

The logarithm of any positive number

*n*to the base*b*is the power*l*to which that base must be raised in order to satisfy the identity*n*=*b*^{l}:*l*= log_{b}*n*.Logarithms to the base 10 are called common logarithms and written log or log

_{10}. Logarithms to the base*e*= 2.7182818284 . . . are called natural (Napierian, hyperbolic) logarithms, and are often written log_{e}or ln. The natural logarithms are the more convenient in any computations involving differentiation