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6.5 - Properties of Logarithms Objective: TSW Apply the properties of logarithms. Properties of Logarithms If M, N, and b are positive numbers and b1, 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 Properties of Logarithms Power Property: log b Mp = p log b M Section 5.5 3 Examples: Expand the following logarithms. 1. log b 2x = y 2. log b 2 = rs 3. log b x2 y3 = Section 5.5 4 Now, condense the following logarithms into one logarithm…Use the properties backwards. 4. 3 log b x 2 log b y 3 log b 4 z Section 5.5 5 5. 1 1 / 2 log b xy 3 log b z log b 3x 2 Section 5.5 6 Properties of Logarithms b is a positive number and b1 log b 1 = 0 since b0 = 1 Example: log 7 1 log b b = 1 , since b1 = b Example: log 7 7 Section 5.5 7 Properties of Logarithms log b bx = x, since bx = bx Example: log 7 72 logbx b = x , since log b x is the exponent to which b is raised to get x log72 Example: 7 log48 4 Section 5.5 8 Examples: Simplify the following: 6. log 9 1 + log 2 8 7. log 8 83 - log 3 1/9 8. log64 6 + log 4 64 9. log 6 6 - log 9 1 Section 5.5 9 Solve for x. 11. 3 log 3 x log 3 8 Section 5.5 10 pgs. 512-513 #’s 725(odds), 29-49(odds)