# Ruby – Find Natural Logarithm – log() Method – Examples & Explanation

`log()` is a method in `CMath` class which is used to find the natural logarithm of a given complex number in Ruby language and if a second argument is given in the code, it will be the base of the logarithm.

## `log()` Method in Ruby

`log()` method exists in Standard CMath Library of Ruby. The purpose of this method is to provide natural logarithm of a given complex number.

## Syntax of the `log()` Method in Ruby

Syntax of `log()` method is:

```cmath.log(x)
```

## Parameter of `log()` Method in Ruby

 Parameter Description `x` Any valid complex number. This parameter is required.

Note: If the `x` parameter is not a complex number, `log()` method will return an `error`.

## Return Value of `log()`

`log()` method will return natural logarithm of a given complex number.

## Ruby `log()` Example 1

``` # import CMath library
require 'cmath'
x = CMath.log(1 + 3i)
puts x
```

Output

` 1.151292546497023+1.2490457723982544i`

## Ruby `log()` Example 2

``` # import CMath library
require 'cmath'
x = CMath.log(10 + 5i, 5)
puts x
```

Output

` 1.5000000000000002+0.2880804567972364i`

## Ruby `log()` Example 3

``` # import CMath library
require 'cmath'
x = CMath.log(-10 + 0i, 5)
puts x
```

Output

` 1.4306765580733933+1.9519812658311715i`

## Ruby `log()` Example 4

``` # import CMath library
require 'cmath'
x = CMath.cosh(a10 - b5i, 5)
puts x
```

Output

` Error`