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Aim: How do we use logarithms to find values of products and quotients?

Aim: How do we use logarithms to find values of products and quotients?. Do Now:. Evaluate to prove or disprove: log (4.5 + 16) or log 20.5 = log 4.5 + log 16 log (4.5  16) = log 4.5 + log 16 log (4.5  16) = log 4.5 - log 16 log (4.5 16 ) = 16 log 4.5.

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Aim: How do we use logarithms to find values of products and quotients?

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  1. Aim: How do we use logarithms to find values of products and quotients? Do Now: Evaluate to prove or disprove: log (4.5 +16) or log 20.5 = log 4.5 + log 16 log (4.5 16) = log 4.5 + log 16 log (4.5 16) = log 4.5 - log 16 log (4.516) = 16 log 4.5

  2. logb MN = logb M + logb N Product Property logb M/N = logb M – logb N Quotient Property logb Mk = k logb M Power Property Properties of Logarithms For any positive numbers M, N, and b, b  1, Each of the following statements is true. log (3 • 5) = log 3 + log 5 log (3 / 5) = log 3 – log 5 log 35 = 5 log 3 Note: loga(M + N) ≠ loga M + loga N Note: base must be the same

  3. Model Problems Write each log expression as a single logarithm log3 20 – log3 4 3 log2x + log2 y log 8 – 2 log 2 + log 3 Quotient Property Power and Product Properties Quotient, Power and Product Properties Expand each log expression = log5x – log5y log5x/y log 3r4 = log 3 + 4 log r

  4. Express in terms of log m and log n Model Problems Rewrite log 7x3 log 7 + 3 log x Expand log2 3xy2 log2 3 + log2x+ 2log2y Condense log 2 - 2log x

  5. ln 6 Model Problems Given ln 2  0.693, ln 3  1.099, and ln 7  1.946, use the properties of logs to approximate a) ln 6 b) ln 7/27 = ln (2 • 3) = ln 2 + ln 3  0.693 + 1.099  1.792 ln 7/27 = ln 7 – ln 27 = ln 7 – 3 ln 3  1.946 – 3(1.099)  -1.351

  6. = log10x1/2 – log10(x + 1)3 = Model Problems Use properties of logarithms to rewrite as the sum and/or difference of logs = ln(3x – 5)1/2 – ln 7 = 1/2 ln(3x – 5) – ln 7 Rewrite the following as a single quantity 1/2 log10x – 3 log10(x + 1)

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