## 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)');