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Properties of Logarithms

Learn about logarithm properties and practice with examples and exercises. Explore multiplication, division, and exponents, and solve various logarithmic equations.

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Properties of Logarithms

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  1. Properties of Logarithms Mrs. King Pre-Calculus

  2. http://apod.nasa.gov/htmltest/gifcity/e.1mil What is e?

  3. Property #1: Multiplication • log (ab) = log a + log b • ln (ab) = ln a + ln b • Examples: • log 3x = log 3 + log x • ln 6 = ln (2x3) = ln 2 + ln 3 • log 8 + log 2 = log (8x2) = log 16 • ln 2 + ln s + ln t = ln (2st)

  4. Property #2: Division • log (a/b) = log a - log b • ln (a/b) = ln a - ln b • Examples: • log ½ = log 1 - log 2 • ln 2/x = ln 2 - ln x • log 8 - log 2 = log (8/2) = log 4 • ln 2 + ln s - ln t = ln ((2s)/t)

  5. Property #3: Exponents • log xn = nlog x • ln xn = nln x • Examples: • log x3 = 3log x • ln 8 = ln 23 = 3ln 2 • log 8 + log 2 = log (8x2) = log 24 =4log 2

  6. Given x=log2, y=log3, and z=log5 • log 6 • log(2*3) • log2+log3 • x + y         • log 12 • log(22*3) • 2log2 + log3 • 2x + y • log(1/9) • log3(-2) • -2log3 • -2y • log(1/81) • log3(-4) • -4log3 • -4y

  7. Homework Page 433 #2-34 even, 53-64 all

  8. Practice: • http://www.regentsprep.org/Regents/math/algtrig/ATE9/LogPrac.htm

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