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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 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 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
Use properties of logarithms to expand the following expressions. • log 2/3 B. log3x/4 C. log 6y D. log3 6xy
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
III. Use log12 3 = 0.4421 and log12 7= 0.7831 to evaluate each expression. a. log12 21 b. log127/3
IV. Solve each equation. A. log2 4 – log2 (x+3) = log2 8