1. 6.5 - Properties of Logarithms Objective: TSW Apply the properties of logarithms.

2. Properties of Logarithms If M, N, and b are positive numbers and b  1, then Product Property: log b MN = log b M + log b N Quotient Property: log b M = log b M - log b N N Section 5.5 2

3. Properties of Logarithms Power Property: log b M p = p log b M Section 5.5 3

4. Examples: Expand the following logarithms. 1. log b 2x = y 2. log b 2 = rs 3. log b x 2 y 3 = Section 5.5 4

5. Now, condense the following logarithms into one logarithm…Use the properties backwards. Section 5.5 5 4.

6. Section 5.5 6 5.

7. Properties of Logarithms b is a positive number and b  1 log b 1 = 0 since b 0 = 1 Example: log 7 1 log b b = 1, since b 1 = b Example: log 7 7 Section 5.5 7

8. Properties of Logarithms log b b x = x, since b x = b x Example: log 7 7 2 b log b x = x, since log b x is the exponent to which b is raised to get x Example: 7 log 7 2 4 log 4 8 Section 5.5 8

9. Examples: Simplify the following: 6. log 9 1 + log 2 8 7. log 8 8 3 - log 3 1/9 8. 6 log 6 4 + log 4 64 9. log 6 6 - log 9 1 Section 5.5 9

10. Solve for x. Section 5.5 10 11.

11. pgs. 512-513 #’s 7- 25(odds), 29-49(odds)