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8­4 Properties of Logarithms 2011 April 27, 2011 8­4 Properties of Logarithms Objective: Discover and use the properties of logarithms. 1 8­4 Properties of Logarithms 2011 April 27, 2011 Check Skills You'll Need Simplify each expression. 1. log2 4 + log2 8 2. log3 9 ­ log3 27 3. log2 16/log2 64 Evaluate each expression for x = 3. 4. x3 ­ x 5. x5 x2 6. x6/x9 7. x3 + x2 2 8­4 Properties of Logarithms 2011 April 27, 2011 With your partner or group, complete the Properties of Logarithms Activity. 3 8­4 Properties of Logarithms 2011 April 27, 2011 Use a calculator to find each answer. 1. log3 + log5 = 5. log(3 5) = 2. log1 + log7 = 6. log(1 7) = 3. log2 + log4 = 7. log(2 4) = 4. log10 + log2 = 8. log(10 2) = ∎ ∎ ∎ ∎ Explain the pattern. 4 8­4 Properties of Logarithms 2011 April 27, 2011 5 8­4 Properties of Logarithms 2011 April 27, 2011 From your activity, you should have discovered the following properties: You can use the properties of logarithms to rewrite logarithmic expressions. 6 8­4 Properties of Logarithms 2011 April 27, 2011 Identifying the Properties of Logarithms State the property or properties used to rewrite each expression: a. log2 8 ­ log2 4 = log2 2 b. logb x3y = 3 logb x + logb y 7 8­4 Properties of Logarithms 2011 April 27, 2011 Simplifying Logarithms Write each logarithmic expression as a single logarithm. a. log3 20 ­ log3 4 b. 3 log2 x + log2 y c. 3 log 2 + log 4 ­ log 16 8 8­4 Properties of Logarithms 2011 April 27, 2011 Expanding Logarithms Expand each logarithm. x a. log5 ( ) y b. log 3r4 c. log2 7b y 2 d. log ( ) 3 e. log7 a3b4 f. log √3b 9 8­4 Properties of Logarithms 2011 April 27, 2011 HOMEWORK Practice 8­4 10