6.3 Logarithmic Functions

Change exponential expression into an equivalent logarithmic expression. Change logarithmic expression into an equivalent exponential expression.

Domain of logarithmic function = Range of exponential function = Range of logarithmic function = Domain of exponential function =

(0, 1) (1, 0) y = x

(1, 0) (0, 1) a > 1 y = x

1. The x-intercept of the graph is 1. There is no y-intercept. 2. The y-axis is a vertical asymptote of the graph. 3. A logarithmic function is decreasing if The graph is smooth and continuous, with no corners or gaps. Properties of the Graph of a Logarithmic Function

The Natural Logarithm

(1, 0) (e, 1)

(4, 0) (e + 3, 1) x = 3

The Common Logarithmic Function (base=10)

Logarithmic Equations