Definition:Natural Logarithm/Positive Real/Definition 1

Definition
The (natural) logarithm of $x$ is the real-valued function defined on $\R_{>0}$ as:
 * $\ds \forall x \in \R_{>0}: \ln x := \int_1^x \frac {\d t} t$

Also see

 * Equivalence of Definitions of Real Natural Logarithm