Sullivan%20Algebra%20and%20Trigonometry:%20Section%206.4%20Logarithmic%20Functions

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Sullivan Algebra and Trigonometry Section
6.4Logarithmic Functions

• Objectives of this Section
• Change Exponential Expressions to Logarithmic
  Expressions and Visa Versa
• Evaluate the Domain of a Logarithmic Function
• Graph Logarithmic Functions
• Solve Logarithmic Equations

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If au av, then u v
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The Logarithmic Function is the inverse of the
exponential function. Therefore
Domain of logarithmic function Range of
exponential function (0, )
Range of logarithmic function Domain of
exponential function (- , )
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The graph of a log function can be obtained using
the graph of the corresponding exponential
function. The graphs of inverse functions are
symmetric about y x.
(0, 1)
(1, 0)
a gt 1
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(0, 1)
(1, 0)
0 lt a lt 1
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1. The x-intercept of the graph is 1. There is
no y-intercept.
2. The y-axis is a vertical asymptote of the
graph.
3. A logarithmic function is decreasing if 0
lt a lt 1 and increasing if a gt 1.
4. The graph is smooth and continuous, with no
corners or gaps.
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The logarithmic function with base e is called
the natural logarithm. This function occurs so
frequently it is given its own symbol ln
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(e, 1)
(1, 0)
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x 3
(e 3, 1)
(4, 0)
Domain x gt 3 (since x - 3 gt 0) Range All Real
Numbers Vertical Asymptote x 3
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To solve logarithmic equations, first rewrite the
equation in exponential form.
Example Solve