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8-4 Properties of Logarithms

8-4 Properties of Logarithms. p. 446. Properties of Logarithms. For any positive numbers, M, N, and b, b≠1. log b M ∙ N = log b M + log b N. log b M / N = log b M – log b N. log b M x = x ∙log b M. Simplifying Logarithms. Example 1

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8-4 Properties of Logarithms

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  1. 8-4 Properties of Logarithms p. 446

  2. Properties of Logarithms For any positive numbers, M, N, and b, b≠1. logbM∙N= logbM+ logbN logbM/N = logbM– logbN logbMx= x∙logbM

  3. Simplifying Logarithms Example 1 Write each logarithmic expression as a single logarithm. = log20 = log4∙5 log4+ log5 = log20 a. b. c. log332 – log38 = log332/8 = log34 = log34 logz2 = 2logz = 2logz

  4. Simplifying Logarithms Example 1 Write each logarithmic expression as a single logarithm. logb1/8 +3 logb4 e. = logb1/8 + logb43 = logb(1/8)(43) = logb(1/8)(64) = logb8 = logb8

  5. Simplifying Logarithms Example 2 Expand each logarithm. = log325∙x5 log3(2x)5 a. = log325+ log3x5 = 5log32 + 5log3x = 5log32 + 5log3x

  6. Simplifying Logarithms Example 2 Expand each logarithm. = log88∙(3a5) log88 b. = log88 +log8 (3a5) = log88 + log8 3∙a = log88 + log8 3+log8 a = log88 + 1/2log8 3+5/2log8 a = log88 + 1/2log8 3+5/2log8 a

  7. Homework p. 449 #11 – 29 odd

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