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 – 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 § 9.4 Properties of Logarithms

4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-4 Properties of Logarithms Argument In the logarithmic expression log a x, x is called the argument of the logarithm. Logarithmic Expression Argument

5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-5 Use the Product Rule for Logarithms Product Rule for Logarithms For positive real numbers x, y, and a, a ≠ 1, The logarithm equals the sum of the logarithms of the factor. Examples of Property 1 Property 1

6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-6 Use the Quotient Rule for Logarithms Quotient Rule for Logarithms For positive real numbers x, y, and a, a ≠ 1, The logarithm of a quotient equals the logarithm of the numerator minus the logarithm of the denominator. Examples of Property 2 Property 2

7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-7 Use the Power Rule for Logarithms Power Rule for Logarithms If x and a are positive real number, a ≠ 1, and n is any real number, then The logarithm of a number raised to an exponent equals the exponent times the logarithm of the number. Examples of Property 3 Property 3

8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-8 Examples Example Use properties 1 through 3 to expand. Quotient Rule Product Rule Power Rule

9 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-9 Use Additional Properties of Logarithms Additional Properties of Logarithms If a > 0 and a ≠ 1, then Examples of Property 4 Property 4 Property 5 Examples of Property 5