# 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

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.

### Notation

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

### Graph of Logarithm Base 2

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 every time 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

### Graph of Logarithm Base 3

Below is the graph of the logarithm function with a base of 3. Note, that every time 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