Ch. 8.4 Properties of Logarithms

Properties of Logariths For any positive numbers, M, N, and b, b ≠ 1 Product Property Quotient Property Power Property

State the property or properties used to rewrite each expression. a. log 6 = log 2 + log 3 Product Property: log 6 = log (23) = log 2 + log 3 b. log b = 2 log b x – log b y x2yx2y Quotient Property: log b = log b x 2 – log b y x2yx2y Power Property: log b x 2 – log b y = 2 log b x – log b y ALGEBRA 2 LESSON 8-4 Properties of Logarithms 8-4

P. 447 Check Understanding 1 A and B

Write each logarithmic expression as a single logarithm. a. log 4 64 – log 4 16 = log 4 4 or 1Simplify. log 4 64 – log 4 16 = log 4 Quotient Property b. 6 log 5 x + log 5 y 6 log 5 x + log 5 y = log 5 x 6 + log 5 yPower Property = log 5 (x 6 y)Product Property So log 4 64 – log 4 16 = log 4 4, and 6 log 5 x + log 2 y = log 5 (x 6 y). ALGEBRA 2 LESSON 8-4 Properties of Logarithms 8-4

Check Understanding P A

Expand each logarithm. a. log 7 tutu b. log(4p 3 ) log(4p 3 ) = log 4 + log p 3 Product Property = log log pPower Property ALGEBRA 2 LESSON 8-4 Properties of Logarithms 8-4 log 7 = log 7 t – log 7 uQuotient Property tutu

Check Understanding P. 447 # 3a - c

Homework Page 449, #2 – 26 even, 34 – 46 even