3.2 Logarithmic Functions and their Graphs

1. 3.2 Logarithmic Functions and their Graphs Students will recognize and evaluate logarithmic functions with base a. Students will graph logarithmic functions. Students will recognize, evaluate, and graph natural logarithmic functions. Students will use logarithmic functions to model and solve real-life problems.

2. Logarithm Conversion If then is called the common logarithm, it means is called the natural logarithm, it means

3. Example 1 Use the logarithm conversion to evaluate each logarithm at the indicated value of x. a. b. c. d.

4. Example 2 Use a calculator to evaluate the function at each value of x. a. x=10 b. x=2.5 c. x=-2 d.

5. Properties of Logarithms 1. 2. 3. 4.

6. Example 3 Solve for x. a. b. Simplify. c.

7. y 2 x –2 Example 4 In the same coordinate plane, sketch the graph of each function by hand. • b.

8. y 2 x –2 Example 5 Each of the following graphs is a transformation of • b.

9. Example 6 Use a calculator to evaluate the function where: • b. c.

10. Example 7 Use the properties of natural logarithms to rewrite each expression. a) b) c) d)

11. Example 8 Find the domain of each function • f(x) = ln (x – 2) b. g(x) = ln (2 – x)