Logarithmic Function

The logarithmic function in base a is the inverse function of the exponential function in base a.

Logarithmic Function

Logarithmic Properties

Examples

Logarithmic Function

x log
1/8 -3
1/4 -2
1/2 -1
1 0
2 1
4 2
8 3

Graph of Logarithmic Function

Logarithmic Function

x Logarithmic Functions
1/8 3
1/4 2
1/2 1
1 0
2 −1
4 −2
8 −3

Logarithmic Function

Properties

Domain: Any Real Number

Range: Any Real Number

It is continuous.

The points (1, 0) and (a, 1) belong to the graph.

Increasing if a > 1.

Decreasing if a < 1.

The graph of the logarithmic function is symmetrical (with respect to the bisector of the 1st and 3rd quadrant) to the graph of the exponential function, as they are the inverse functions of each other.

Exponential and Logarithmic Functions

Symmetrical Functions


Logarithmic Functions Worksheet