\begin{definition}[Definition:Natural Logarithm/Positive Real/Definition 2]
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:
:$\ln x = \log_e x$
\end{definition}