Returns the logarithm with a base of b of the number x.
log(x,b)| Name | Description |
|---|---|
| x | the input number |
| b | the base of the logarithm |
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) = 2The 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) = 3Below 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) = 3The 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.