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Section 8.5

Section 8.5. Properties of Logarithms. log b (MN)= log b M + log b N Ex: log 4 (15)= log 4 5 + log 4 3 log b (M/N)= log b M – log b N Ex: log 3 (50/2)= log 3 50 – log 3 2 log b M r = r log b M Ex: log 7 10 3 = 3 log 7 10

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Section 8.5

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  1. Section 8.5 Properties of Logarithms

  2. logb(MN)= logbM + logbN Ex: log4(15)= log45 + log43 logb(M/N)= logbM – logbN Ex: log3(50/2)= log350 – log32 logbMr = r logbM Ex: log7 103 = 3 log7 10 logb(1/M) =logbM-1= –1 logbM= – logbM Ex: log11 (1/8) = log11 8-1 = – 1 log11 8 = – log11 8 Properties of Logarithms

  3. Examples:Rewrite in terms of log57 and log53

  4. Examples of Logarithms • Simplify log 7 + log 4 – log 2 = log 7*4 = log 14 2 • Simplify ln e2 = 2 ln e = 2 logee = 2 * 1 = 2 • Simplify e 4 ln 3 - 3 ln 4= e ln 34 - ln 43 = e ln 81/64 = e loge81/64 = 81/64

  5. Expanding Logarithms Expand :

  6. Condensing Logarithms Condense: log 6 + 2 log 2 – log 3 log 6 + 2 log 2 – log 3 = log 6 + log 22 – log 3

  7. logam logbm = -------- logab log712 = log 12 log 7 OR Change-of-Base Formula • log712= ln 12 • ln 7

  8. Example • Evaluate: 1) log37 = 2) log410 =

  9. Assignment Section 8.5: page 496 – 497 # 15 – 72 (every 3rd)

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