1. Copyright © 2011 Pearson, Inc. 3.3 Logarithmic Functions and Their Graphs

2. Copyright © 2011 Pearson, Inc. Slide 3.3 - 2 What you’ll learn about Inverses of Exponential Functions Common Logarithms – Base 10 Natural Logarithms – Base e Graphs of Logarithmic Functions Measuring Sound Using Decibels … and why Logarithmic functions are used in many applications, including the measurement of the relative intensity of sounds.

3. Copyright © 2011 Pearson, Inc. Slide 3.3 - 3 Changing Between Logarithmic and Exponential Form

4. Copyright © 2011 Pearson, Inc. Slide 3.3 - 4 Inverses of Exponential Functions

5. Copyright © 2011 Pearson, Inc. Slide 3.3 - 5 Basic Properties of Logarithms

6. Copyright © 2011 Pearson, Inc. Slide 3.3 - 6 An Exponential Function and Its Inverse

7. Copyright © 2011 Pearson, Inc. Slide 3.3 - 7 Common Logarithm – Base 10 Logarithms with base 10 are called common logarithms. The common logarithm log 10 x = log x. The common logarithm is the inverse of the exponential function y = 10 x.

8. Copyright © 2011 Pearson, Inc. Slide 3.3 - 8 Basic Properties of Common Logarithms

9. Copyright © 2011 Pearson, Inc. Slide 3.3 - 9 Example Solving Simple Logarithmic Equations

10. Copyright © 2011 Pearson, Inc. Slide 3.3 - 10 Example Solving Simple Logarithmic Equations

11. Copyright © 2011 Pearson, Inc. Slide 3.3 - 11 Basic Properties of Natural Logarithms

12. Copyright © 2011 Pearson, Inc. Slide 3.3 - 12 Graphs of the Common and Natural Logarithm

13. Copyright © 2011 Pearson, Inc. Slide 3.3 - 13 Example Transforming Logarithmic Graphs

14. Copyright © 2011 Pearson, Inc. Slide 3.3 - 14 Example Transforming Logarithmic Graphs

15. Copyright © 2011 Pearson, Inc. Slide 3.3 - 15 Example Transforming Logarithmic Graphs

16. Copyright © 2011 Pearson, Inc. Slide 3.3 - 16 Example Transforming Logarithmic Graphs

17. Copyright © 2011 Pearson, Inc. Slide 3.3 - 17 Decibels

18. Copyright © 2011 Pearson, Inc. Slide 3.3 - 18 Quick Review

19. Copyright © 2011 Pearson, Inc. Slide 3.3 - 19 Quick Review Solutions