\begin{definition}[Definition:Natural Logarithm/Positive Real/Definition 3]
Let $x \in \R$ be a real number such that $x > 0$.
The '''(natural) logarithm''' of $x$ is defined as:
:$\ds \ln x := \lim_{n \mathop \to \infty} n \paren {\sqrt [n] x - 1}$
\end{definition}