Properties of Logarithms

1. Properties of Logarithms These properties are based on rules of exponents since logs = • exponents

2. I. Because in exponential form (any number to the zero power = 1) 5 to what power = 1? 0 = = Example: Example: 0

3. II. Because in exponential form (any number to the first power is itself) 5 to what power = 5? 1 = = Example: Example: 1

4. III. Product Rule Because in exponential form 6 = = Examples: =

5. IV. Quotient Rule Because in exponential form = = Examples: =

6. V. Power Rule Because in exponential form = = Examples:

7. VI. Change of Base Formula = Example: These properties remain the same when working with the natural log.

8. Use properties of logarithms to determine if each of the following is true or false. Check your answers using your calculator True or False: True False True True False False False False True True True True

9. Use the properties of logs to expand the following expressions: 1. 1. Apply Product Rule: 2. Apply Power Rule:

10. Use the properties of logs to expand the following expressions: 2. 1. Apply Product Rule: 2. Apply Power Rule:

11. Use the properties of logs to expand the following expressions: 3. 1. Apply Quotient Rule: 2. Apply Product Rule:

12. Use the properties of logs to expand the following expressions: 4. 1. Change radical to exponential form: 3. Apply Power Rule: 2. Apply Product Rule:

13. Use the properties of logs to expand the following expressions: 5. 3. Apply Power Rule: 2. Apply Product Rule:

14. Write as a single logarithmic expression. 5. 2. Apply Reverse Quotient Rule: 1. Apply Reverse Power Rule: 3. Change to radical form

15. Write as a single logarithmic expression. 6. 2. Simplify 1. Apply Reverse Product Rule:

16. Write as a single logarithmic expression. 6. 1. Apply Reverse Power Rule: 2. Apply Reverse Product Rule:

17. Practice Time