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:


 * $ \displaystyle \ln x := \lim_{n \to \infty} n \left({ \sqrt[n]{ x } - 1 }\right)$

Also see

 * Equivalence of Definitions of Natural Logarithm