# 7-5 Properties of Logarithms - Denton ISD

7-5 PROPERTIES OF LOGARITHMS Rolling them out and Wrapping them up Definitions 1. Product Property 2. Quotient Property 3. Power Property The above will be on the quiz! Product Property

b, m, & n must be positive numbers and b 1 log b mn = log b m + log b n Examples: log 21 = log 4 (3 7) = log 4 3 + log 4 7 log 3 27 = log 3 (3 * 9) = log 3 3 + log 3 9 = 1+2 = 3 log 3 4x = log 3 4 + log 3 x 4 Quotient Rule b, m, & n must be positive numbers and b 1 log

Examples: m = log b m log b n n b log 4 log 3 3 = log 4 3 log 4 7 7 2 = log 3 2 log 3 x x Notice the numerator is listed first and the denominator is subtracted from it

Power Property b, m, & n must be positive numbers and b 1 log b mn = n log b m Examples: log 49 = log 4 72 = 2 log 4 7 log 2 512 = log 2 83 = 3 log 2 8 =33 =9 4 Using properties to expand an expression log 5x=3 log 6 5x3 log 6 y

y 6 = log = log 6 6 5 + log 5 + 3 log 6 6 Quotient Property x3 log x log 6 y 6

y Product Property Power Property Using properties to condense an expression 5 log 4 2 + 7 log 4 x 4 log log 4 25 + log 4 x7 log 4 y4 log 4 25x7 log 4 y4 log 7 32x 2 x = log 4 4 y y4 5 4 7

4 y Power Property Product Property Quotient Property & Simplify Change of Base Formula log 3 8 =log 8 log 3 1.893 0.903 1 0.477 1

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