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.
