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Properties of Logarithmic Functions

Properties of Logarithmic Functions. Properties of Logarithms. For m > 0, n > 0, b > 0, and b  1:. Product Property. log b (mn) = log b m + log b n. Example 1. given: log 5 12  1.5440. log 5 10  1.4307. log 5 120 =. log 5 (12)(10). = log 5 12 + log 5 10.

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Properties of Logarithmic Functions

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  1. Properties of Logarithmic Functions

  2. Properties of Logarithms For m > 0, n > 0, b > 0, and b  1: Product Property logb (mn) = logb m + logb n

  3. Example 1 given: log5 12  1.5440 log5 10  1.4307 log5 120 = log5 (12)(10) = log5 12 + log5 10 1.5440 + 1.4307 2.9747

  4. logb = logb m – logb n m n Properties of Logarithms For m > 0, n > 0, b > 0, and b  1: Quotient Property

  5. 12 = log5 10 Example 2 given: log5 12  1.5440 log5 10  1.4307 log5 1.2 = log5 12 – log5 10 1.5440 – 1.4307 0.1133

  6. Properties of Logarithms For m > 0, n > 0, b > 0, and any real number p: Power Property logb mp = p logb m

  7. Example 3 given: log5 12  1.5440 log5 10  1.4307 log5 1254 5x = 125 = 4 log5 125 53 = 125 =4  3 x = 3 = 12

  8. Practice Write each expression as a single logarithm. 1) log2 14 – log2 7 2) log3 x + log3 4 – log3 2 3) 7 log3 y – 4 log3 x

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