1. MAT150 Unit 4-2: Logarithmic Functions; Properties of Logarithms Copyright ©2013 Pearson Education, Inc.

2. Objectives  Graph and evaluate logarithmic functions  Convert equations to logarithmic and exponential forms  Evaluate and apply common logarithms  Evaluate and apply natural logarithms  Apply logarithmic properties

4. Example Write each of the following exponential equations in logarithmic form. Solution a. 4 2 = 16 b. c. d.

5. Example Write each of the following logarithmic equations in exponential form. Solution a. log 2 32 = 5 b. log 10 0.00001 = –5 c. log 8 1 = 0

8. Example Explain how the graph of each of the following functions compares with the graph of y = log x, find the domain, and graph each function. a. y = log(x + 3) b. y = 4 + log(x – 2) c.

9. Example (cont) a. y = log(x + 3) Solution

10. Example (cont) b. y = 4 + log(x – 2) Solution

11. Example (cont) c. Solution

13. Example Projections from 2010 to 2050 indicate that the percent of U.S. adults with diabetes (diagnosed and undiagnosed) can be modeled by p(x) = –12.975 + 11.851 ln x, where x is the number of years after 2000. a. Graph this function. b. Is the function increasing or decreasing? What does this mean in the context of the application? c. What does this model predict the percent of U.S. adults with diabetes will be in 2022? d. Use the graph to estimate the year in which this model predicts the percent will reach 33%.

14. Example (cont) Solution a. Graph this function. b.

15. Example (cont) c. d.

17. Example

18. Rewrite each of the following expressions as a single logarithm. a. log 5 x + 3log 5 y b. Solution

19. Example (cont) Rewrite each of the following expressions as a single logarithm. c. Solution