1. Sullivan Algebra and Trigonometry: Section 6.4 Logarithmic Functions
Objectives of this Section
Change Exponential Expressions to Logarithmic Expressions and Visa Versa
Evaluate the Domain of a Logarithmic Function
Graph Logarithmic Functions
Solve Logarithmic Equations

3. If au= av, then u = v

4. The Logarithmic Function is the inverse of the exponential function
The Logarithmic Function is the inverse of the exponential function. Therefore:
Domain of logarithmic function = Range of exponential function = (0, )
Range of logarithmic function = Domain of exponential function = (- , )

5. The graph of a log function can be obtained using the graph of the corresponding exponential function. The graphs of inverse functions are symmetric about y = x.
(0, 1)
(1, 0)
a > 1

6. (0, 1)
(1, 0)
0 < a < 1

7. 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 logarithmic function with base e is called the natural logarithm
The logarithmic function with base e is called the natural logarithm. This function occurs so frequently it is given its own symbol: ln

9. (e, 1)
(1, 0)

10. Domain: x > 3 (since x - 3 > 0) Range: All Real Numbers
(4, 0)
Domain: x > 3 (since x - 3 > 0)
Range: All Real Numbers
Vertical Asymptote: x = 3

11. To solve logarithmic equations, first rewrite the equation in exponential form.
Example: Solve