1. Section 4 Chapter 10

2. 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives 2 3 4 Properties of Logarithms Use the product rule for logarithms. Use the quotient rule for logarithms. Use the power rule for logarithms. 10.4

3. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Use the product rule for logarithms. Objective 1 Slide 10.4- 3

4. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Product Rule for Logarithms If x, y, and b are positive real numbers, where b ≠ 1, then the following are true. log b xy = log b x + log b y That is, the logarithm of a product is the sum of the logarithm of the factors. Slide 10.4- 4 Use the produt rule for logarithms. The word statement of the product rule can be restated by replacing “logarithm” with “exponent.” The rule then becomes the familiar rule for multiplying exponential expressions: The exponent of a product is the sum of the exponents of the factors.

5. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Use the product rule to rewrite each logarithm. Slide 10.4- 5 CLASSROOM EXAMPLE 1 Using the Product Rule Solution:

6. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Use the quotient rule for logarithms. Objective 2 Slide 10.4- 6

7. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Quotient Rule for Logarithms If x, y, and b are positive real numbers, where b ≠ 1, then the following is true. That is, the logarithm of a quotient is the difference between the logarithm of the numerator and the logarithm of the denominator. Slide 10.4- 7 Use the quotient rule for logarithms.

8. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Use the quotient rule to rewrite each logarithm. Slide 10.4- 8 CLASSROOM EXAMPLE 2 Using the Quotient Rule Solution:

9. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Use the power rule for logarithms. Objective 3 Slide 10.4- 9

10. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Power Rule for Logarithms If x and b are positive real numbers, where b ≠ 1, and if r is any real number then the following is true. That is, the logarithm of a number to a power equals the exponent times the logarithm of the number. Slide 10.4- 10 Use the power rule for logarithms.

11. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Use the power rule to rewrite each logarithm. Assume a > 0, b > 0, x > 0, a ≠ 1, and b ≠ 1. Slide 10.4- 11 CLASSROOM EXAMPLE 3 Using the Power Rule Solution:

12. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Special Properties If b > 0 and b ≠ 1, then the following are true. Slide 10.4- 12 Use the power rule for logarithms.

13. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Use the special properties to find each value. Slide 10.4- 13 CLASSROOM EXAMPLE 4 Using the Special Properties Solution:

14. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Properties of Logarithms If x, y, and b are positive real numbers, where b ≠ 1, and r is any real number, then the following are true. Product Rule log b xy = log b x + log b y Quotient Rule Power Rule Special Properties Slide 10.4- 14 Use the power rule for logarithms.