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Ch. 8.4 Properties of Logarithms

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. x 2 y. x 2 y. b. log b = 2 log b x – log b y. Quotient Property: log b = log b x 2 – log b y.

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Ch. 8.4 Properties of Logarithms

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  1. Ch. 8.4 Properties of Logarithms

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

  3. x2 y x2 y b. logb = 2 logbx– logby Quotient Property: logb = logbx2– logby Properties of Logarithms ALGEBRA 2 LESSON 8-4 State the property or properties used to rewrite each expression. a. log 6 = log 2 + log 3 Product Property: log 6 = log (2•3) = log 2 + log 3 Power Property: logbx2– logby = 2 logbx– logby 8-4

  4. P. 447 Check Understanding 1 A and B

  5. 64 16 log4 64 – log4 16 = log4Quotient Property Properties of Logarithms ALGEBRA 2 LESSON 8-4 Write each logarithmic expression as a single logarithm. a. log4 64 – log4 16 = log4 4 or 1 Simplify. b. 6 log5x + log5y 6 log5x + log5y = log5 x6 + log5 y Power Property = log5 (x6y) Product Property So log4 64 – log4 16 = log4 4, and 6 log5x + log2y = log5 (x6y). 8-4

  6. Check Understanding P. 447 2A

  7. a. log7 t u t u log7 = log7t– log7uQuotient Property Properties of Logarithms ALGEBRA 2 LESSON 8-4 Expand each logarithm. b. log(4p3) log(4p3) = log 4 + log p3Product Property = log 4 + 3 log pPower Property 8-4

  8. Check Understanding P. 447 # 3a - c

  9. Homework • Page 449, #2 – 26 even, 34 – 46 even

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