3.4 Properties of Logarithmic Functions

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Presentation transcript:

3.4 Properties of Logarithmic Functions

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 = c logbR Ex) log2x-2 =

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

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

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

Use the change-of-base formula and your calculator to evaluate the logarithm: You Try! Log8175 Log0.512

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.

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

Describe how to transform the graph of f(x) = ln x into the graph of the given function: h(x) = log1/4x

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

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