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10.3 Properties of Logarithms

10.3 Properties of Logarithms. Algebra II w/trig. Logarithmic expressions can be rewritten using the properties of logarithms. Product Property: the log of a product is the sum of the logs of the factors log b mn = log b m + log b n

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10.3 Properties of Logarithms

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  1. 10.3 Properties of Logarithms Algebra II w/trig

  2. Logarithmic expressions can be rewritten using the properties of logarithms. Product Property: the log of a product is the sum of the logs of the factors logbmn =logb m + logb n Quotient Property: the log of a quotient is the difference of the logs of the numerator and denominator logbm/n = logb m – logb n Power Property: the log of an expression raised to an exponent is the exponent times the log of the expression logb mx = x logb m

  3. Use properties of logarithms to expand the following expressions. • log 2/3 B. log3x/4 C. log 6y D. log3 6xy

  4. E. log6 36x2 F. log3 x2y

  5. II. Use properties of logarithmic to write each logarithmic expression as a single logarithm. • log3 13 + log3 3 • log58 + log5 x • 3log7 x – 5log7 y

  6. III. Use log12 3 = 0.4421 and log12 7= 0.7831 to evaluate each expression. a. log12 21 b. log127/3

  7. C. log12 49 D. log12 36

  8. IV. Solve each equation. A. log2 4 – log2 (x+3) = log2 8

  9. B. log10 (x+3) – log10 (2x-1) = log10 2

  10. C. log3 (c+3) – log3 (4c-1)

  11. D. 1/3log4 x = log4 4

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