Title: Sullivan%20Algebra%20and%20Trigonometry:%20Section%206.4%20Logarithmic%20Functions
1Sullivan 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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3If au av, then u v
4The 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 (- , )
5The 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
6(0, 1)
(1, 0)
0 lt a lt 1
71. 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.
8The logarithmic function with base e is called
the natural logarithm. This function occurs so
frequently it is given its own symbol ln
9(e, 1)
(1, 0)
10x 3
(e 3, 1)
(4, 0)
Domain x gt 3 (since x - 3 gt 0) Range All Real
Numbers Vertical Asymptote x 3
11To solve logarithmic equations, first rewrite the
equation in exponential form.
Example Solve