# 1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-1 Exponential and Logarithmic Functions Chapter 9.

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1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-1 Exponential and Logarithmic Functions Chapter 9

2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-2 9.1 – Composite and Inverse Functions 9.2 – Exponential Functions 9.3 – Logarithmic Functions 9.4 – Properties of Logarithms 9.5 – Common Logarithms 9.6 – Exponential and Logarithmic Equations 9.7 – Natural Exponential and Natural Logarithmic Functions Chapter Sections

3 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-3 § 9.6 Exponential and Logarithmic Equations

4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-4 Solve Exponential and Logarithmic Equations Properties for Solving Exponential and Logarithmic Equations a)If x = y, then a x = a y. b)If a x = a y, then x = y. c)If x = y, then log b x = log b y (x > 0, y > 0). d)If log b x=log b y, then x = y (x > 0, y > 0).

5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-5 Solve Exponential and Logarithmic Equations Example Solve the equation. Property 6b

6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-6 Solve Exponential and Logarithmic Equations Example Solve Property 6d

7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-7 Solve Applications Example If there are initially 1000 bacteria in a culture, and the number of bacteria doubles each hour, the number of bacteria after t hours can be found by the formula How long will it take for the culture to grow to 30,000 bacteria? continued

8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-8 Solve Applications We want to find the value for t. To accomplish this we will use logarithms. Begin by taking the logarithm of both sides of the equation. continued

9 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-9 Solve Applications It will take about 4.91 hours for the culture to grow 30,000 bacteria.