# Natural Logarithm Function

## Function

`ln(x)`

## Summary

Returns the natural logarithm of the number x.

## Input

Name | Description |
---|---|

x | the input number |

## Output

## Explanation

The natural logarithm function describes the behavior of exponential decay which is the opposite of exponential growth. The natural logarithm function can be formally defined by the area under the hyperbola from to , or as discussed below it can also be defined as the inverse of the exponential function.

### Alternative Definition

The natural logarithm function can also be defined as the inverse of the exponential function. Recall that the output of the exponential function grows proportionally to its current value. So inversely, the value of the natural logarithm is proportional to its current rate of decay.

### Properties of the Natural Logarithm

The natural logarithm is the same as the logarithm function with a base of , eulers number.