Logarithmic Functions

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

Logarithmic Functions

Logarithmic Functions

log

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

Logarithmic Function

Logarithmic Functions

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

Logarithmic Function

Properties of Logarithmic Functions

Domain: R +

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.

Symmetrical Functions

Symmetrical Functions