Definition:Euler's Number/Base of Logarithm

Definition
The number $e$ can be defined as the number satisfied by:
 * $\ln e = 1$.

where $\ln e$ denotes the natural logarithm of $e$.

That $e$ is unique follows from Logarithm is Strictly Increasing and Strictly Concave.

Also see

 * Equivalence of Definitions of Euler's Number