1. 4.3 Logarithmic Functions

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

4. Domain of logarithmic function = Range of exponential function =
Range of logarithmic function = Domain of exponential function =

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

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

7. 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 < a < 1 and increasing if a > 1.
4. The graph is smooth and continuous, with no corners or gaps.

8. The Natural Logarithm

10. (e, 1)
(1, 0)

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

13. The Common Logarithmic Function
(base=10)

14. Logarithmic Equations