Definition:Natural Logarithm/Positive Real/Definition 1

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

Let $t$ be in the closed (real) interval $\closedint 1 x$.

The (natural) logarithm of $x$ is defined as the real-valued function:

$\ln: \R_{>0} \to \R$

Such that:


 * $\ds \ln x := \int_1^x \frac {\d t} t$

Also see

 * Equivalence of Definitions of Real Natural Logarithm