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3.4 Properties of Logarithmic Functions

3.4 Properties of Logarithmic Functions. Properties of Logarithms. Product Rule: log b (RS ) = log b R + log b S Ex) ln 8x = Quotient Rule: log b (R /S) = log b R – log b S Ex) log (3/x) = Power Rule: log b R c = c log b R Ex) log 2 x -2 =.

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3.4 Properties of Logarithmic Functions

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  1. 3.4 Properties of Logarithmic Functions

  2. Properties of Logarithms • Product Rule: logb(RS) = logbR + logbS Ex) ln 8x = • Quotient Rule: logb(R/S) = logbR – logbS Ex) log (3/x) = • Power Rule: logbRc = clogbR Ex) log2x-2 =

  3. You Try! Write the expression as a sum or difference of logarithms or multiples of logarithms • ln 9y • log2y5 • ln (x2/y3)

  4. You Try! Write the expression as a single logarithm • log5x + log5y • 2 lnx + 3 ln y • 4 log (xy) – 3log (yz)

  5. Change-of-Base Formula For positive real numbers a, b, and x with a ≠1 and b ≠1, or

  6. Use the change-of-base formula and your calculator toevaluate the logarithm: • Log27 You Try! • Log8175 • Log0.512

  7. Graphing Logarithmic functions • If b > 1, the graph of g(x) = logbx is a vertical stretch or shrink of the graph of ln (x) by the factor of 1/ ln b. • If 0 < b < 1, a reflection across the x-axis is required as well.

  8. Describe how to transform the graph of f(x) = lnx into the graph of the given function: g(x) = log5x

  9. Describe how to transform the graph off(x) = lnx into the graph of the given function: h(x) = log1/4x

  10. f(x) = ln (x3) • Domain • Range • Continuity • Increasing • Decreasing • Asymptotes • End Behavior

  11. Homework Pg. 317 (4, 6, 12, 20, 22, 28, 40, 42, 49)

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