# Logarithmic Function

## Logarithmic Function

Function characterized by a relation in the form f(x) = log$$_{a}$$(x) where a is a strictly positive real number that is different from 1.

### Properties

Exponential functions of base a defined by f(x) = $${a}^{x}$$ and logarithmic functions of base a defined by f(x) = log$$_{a}$$(x) are the inverse of one another.

If a > 1, the function defined by f(x) = $${a}^{x}$$ is strictly increasing in the set of strictly positive real numbers and if 0 < a < 1, it is strictly decreasing in the set of strictly positive real numbers.

### Example

The function f defined in the set of real numbers by the relation f(x) = log$$_{2}$$(x) is a logarithmic function with base 2.

A function f defined in the set of real numbers by the relation f(x) = log$$_{3}$$(x) is a logarithmic function with base 3.