# Logarithm Function

## Summary

Returns the logarithm with a base of b of the number x.

### Syntax

`log(x,b)`

### Arguments

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

x | the input number |

b | the base of the logarithm |

## Usage

` log(8,2) = 3`

` log(9,3) = 2`

` log(27,3) = 3`

` log(1,4) = 0`

` log(4,4) = 1`

` log(16,4) = 2`

` log(81,9) = 2`

The logarithm function is the inverse operation of exponentiation. This is expressed by the two equations below, in both cases the variable represents the base of the operation.

For example, 2 raised to the 3rd power is equal to 8. Inversely, the logarithm base 2 of 8 is equal to 3.

Sometimes the base of the logarithm is written as subscript after the function name.

Below is the graph of the logarithm function with a base of 2. The logarithm with any base, , of 1 will always equal 0. Note, for everytime the input increases by a factor of 2 the output of the function increases by 1.

` log(1,2) = 0`

` log(2,2) = 1`

` log(4,2) = 2`

` log(8,2) = 3`

Below is the graph of the logarithm function with a base of 3. Note, everytime the input increases by a factor of 3 the output of the function increases by 1.

` log(1,3) = 0`

` log(3,3) = 1`

` log(9,3) = 2`

` log(27,3) = 3`

## Natural Logarithm Function

The natural logarithm function is defined as the logarithm function with a base (Euler’s Number).

Sometimes the notation refers to the natural logarithm, but it can also refer implicitly to the . This site will always use the notation or to be explicit.