Definition:Natural Logarithm/Positive Real/Definition 2

Definition
Let $x \in \R$ be a real number such that $x > 0$.

The (natural) logarithm of $x$ is defined as:


 * $\ln x := y \in \R: e^y = x$

where $e$ is Euler's number.

That is:
 * $\ln x = \log_e x$

Also see

 * Equivalence of Definitions of Natural Logarithm