## LOG Natural Logarithm Function

Section: Mathematical Functions

### Usage

Computes the`log`

function for its argument. The general
syntax for its use is
y = log(x)

where `x`

is an `n`

-dimensional array of numerical type.
Integer types are promoted to the `double`

type prior to
calculation of the `log`

function. Output `y`

is of the
same size as the input `x`

. For strictly positive, real inputs,
the output type is the same as the input.
For negative and complex arguments, the output is complex.

### Function Internals

Mathematically, the`log`

function is defined for all real
valued arguments `x`

by the integral

For complex-valued arguments, `z`

, the complex logarithm is
defined as

where `arg`

is the complex argument of `z`

.

### Example

The following piece of code plots the real-valued`log`

function over the interval `[1,100]`

:
--> x = linspace(1,100); --> plot(x,log(x)) --> xlabel('x'); --> ylabel('log(x)');