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4.2_bzca5e

# 4.2_bzca5e - Section 4.2 Logarithmic Functions The...

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Section 4.2 Logarithmic Functions

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The Definition of Logarithmic Functions

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To change from logarithmic form to the more familiar exponential form, use the pattern; y=log means b y b x x =
Example 2 3 Write each equation in the equivalent exponential form. a. 4=log b. x=log 9 x

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Example 4 2 Write each equation in its equivalent logarithmic form. a. b 16 b. 5 x = =
Example 3 36 5 Evaluate. a. log 81 b. log 6 c. log 1

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Basic Logarithmic Properties
8 6 Examples: log 8 1 log 1 0 = = 5 2 7 log 8 Examples: log 7 2 5 8 = =

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The voice balloons should help you see the "undoing" that takes place between the exponential and logarithmic functions in the inverse properties.
Example 3 log 15 3 2 9 1 3 3 Use the properties of logarithms to find the answers. a. 3 b. log 2 c. log 9 d. log

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Graphs of logarithmic Functions

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Example 3 3 Use transformations to graph g(x)=2+log ( 3). Start with log . x x - -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 1 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x y
Example 3 Use transformations to graph g(x)=-log x -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 1 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x y

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4.2_bzca5e - Section 4.2 Logarithmic Functions The...

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