 # 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.

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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 Quotient Property: the log of a quotient is the difference of the logs of the numerator and denominator log b m / n = log b m – log b n Power Property: the log of an expression raised to an exponent is the exponent times the log of the expression log b m x = x log b m

I. Use properties of logarithms to expand the following expressions. A. log 2 / 3 B. log 3 x / 4 C. log 6yD. log 3 6xy

E. log 6 36x 2 F. log 3 x 2 y

II. Use properties of logarithmic to write each logarithmic expression as a single logarithm. a. log 3 13 + log 3 3 b. log 5 8 + log 5 x c. 3log 7 x – 5log 7 y

III. Use log12 3 = 0.4421 and log12 7= 0.7831 to evaluate each expression. a. log 12 21b. log 12 7 / 3

C. log 12 49D. log 12 36

IV. Solve each equation. A. log 2 4 – log 2 (x+3) = log 2 8

B. log 10 (x+3) – log 10 (2x-1) = log 10 2

C. log 3 (c+3) – log 3 (4c-1)

D. 1 / 3 log 4 x = log 4 4

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