Returns the natural logarithm of the number x.

```
ln(x)
```

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

x | the input number |

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.

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.

The natural logarithm is the same as the logarithm function with a base of , Euler’s Number.

The exponential function models exponential growth. The output of the function at any given point is equal to the rate of change at that point. For real number input, the function conceptually returns Euler's number raised to the value of the input.

Euler's number is a naturally occurring number related to exponential growth and exponential decay.