Logarithmic Function
Function characterized by a relation in the form f(x) = log[latex] _{a}[/latex](x) where a is a strictly positive real number that is different from 1.
Properties
Exponential functions of base a defined by f(x) = [latex]{a}^{x}[/latex] and logarithmic functions of base a defined by f(x) = log[latex] _{a}[/latex](x) are the inverse of one another. If a > 1, the function defined by f(x) = [latex]{a}^{x}[/latex] 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[latex] _{2}[/latex](x) is a logarithmic function with base 2.
A function f defined in the set of real numbers by the relation f(x) = log[latex] _{3}[/latex](x) is a logarithmic function with base 3.
