# User:Keith.U/Whatever

Consider the natural logarithm $\ln x$, which is defined on the open interval $\openint 0 {+\infty}$.

$\ln x$ is strictly increasing.
the inverse of $\ln x$ always exists.

The inverse of the natural logarithm function is called the exponential function, which is denoted as $\exp$.

Thus for $x \in \R$, we have:

$y = \exp x \iff x = \ln y$

The exponential function can be defined as a power series:

$\exp x := \displaystyle \sum_{n \mathop = 0}^\infty \frac {x^n} {n!}$