4.3 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 =

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

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

1. The x-intercept of the graph is 1. There is no y-intercept. Properties of the Graph of a Logarithmic Function 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 0 < a < 1 and increasing if a > 1. 4. The graph is smooth and continuous, with no corners or gaps.

The Natural Logarithm

(e, 1) (1, 0)

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

The Common Logarithmic Function (base=10)

Logarithmic Equations