Definition:Natural Logarithm/Positive Real/Definition 3

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

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


 * $\ds \ln x := \lim_{n \mathop \to \infty} n \paren {\sqrt [n] x - 1}$

Also see

 * Equivalence of Definitions of Real Natural Logarithm