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7-5 Properties of Logarithms

7-5 Properties of Logarithms. Rolling them out and Wrapping them up. Definitions. 1. Product Property 2 . Quotient Property 3 . Power Property The above will be on the quiz!. Product Property. b, m, & n must be positive numbers and b ≠ 1 l og b mn = log b m + log b n

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7-5 Properties of Logarithms

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  1. 7-5 Properties of Logarithms Rolling them out and Wrapping them up

  2. Definitions • 1. Product Property • 2. QuotientProperty • 3. Power Property • The above will be on the quiz!

  3. Product Property • b, m, & n must be positive numbers and b ≠ 1 • log bmn = log b m + log b n • Examples: • log 4 21 = log 4 (3 · 7) = log 4 3 + log 4 7 • log 3 27 = log 3 (3 * 9) = log 3 3 + log 3 9 = 1 + 2 = 3 • log 3 4x = log 3 4 + log 3 x

  4. Quotient Rule • b, m, & n must be positive numbers and b ≠ 1 • log b = log b m – log b n • Examples: • log 4 = log 4 3 – log 4 7 • log 3 = log 3 2 – log 3 x • Notice the numerator is listed first and the denominator is subtracted from it m n 3 7 2 x

  5. Power Property • b, m, & n must be positive numbers and b ≠ 1 • log bmn = n log b m • Examples: • log 4 49 = log 4 72 = 2 log 4 7 • log 2 512 = log 2 83 = 3 log 2 8 = 3 · 3 = 9

  6. Using properties to expand an expression • log 6 =log 6 5x3 – log 6 y Quotient Property = log 6 5 + log 6 x3 – log 6 y Product Property = log 6 5 + 3 log 6 x – log 6 y Power Property 5x3 y Using properties to condense an expression • 5 log 4 2 + 7 log 4 x – 4 log 4 y • log 4 25 + log 4 x7 – log 4 y4Power Property • log 4 25x7 – log 4 y4 Product Property • log4 = log 4Quotient Property & Simplify 32x7 y4 25x7 y4

  7. Change of Base Formula • log 3 8 = ≈ • ≈ 1.893 log 8 log 3 0.9031 0.4771

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