1. Chapter 4 Exponential and Logarithmic Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 4.3 Properties of Logarithms

2. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 2 Use the product rule. Use the quotient rule. Use the power rule. Expand logarithmic expressions. Condense logarithmic expressions. Use the change-of-base property. Objectives:

3. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 3 The Properties of Logs Let b, M, and N be positive real numbers with b 1. The Product Rule: The Quotient Rule: The Power Rule:

4. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 4 Example: Expanding Logarithmic Expressions Use logarithmic properties to expand the expression as much as possible:

5. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 5 Example: Expanding Logarithmic Expressions Use logarithmic properties to expand the expression as much as possible:

6. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 6 Example: Condensing Logarithmic Expressions Write as a single logarithm: a) b) c)

7. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 7 The Change-of-Base Property For any logarithmic bases a and b, and any positive number M, The logarithm of M with base b is equal to the logarithm of M with any new base divided by the logarithm of b with that new base. **Usually only use two special cases….

8. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 8 The Change-of-Base Property: Introducing Common and Natural Logarithms Introducing Common Logarithms Introducing Natural Logarithms

9. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 9 Example: Changing Base to Common Logarithms Use change of base to evaluate