Logarithmic Functions

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Logarithmic Functions
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One one Function
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(3,8)
(2,4)
(1,2)
(8,3)
(-1,1/2)
(4,2)
(2,1)
(-2,1/4)
(1/2,-1)
(-1/4,-2)
Inverse of
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The inverse of is the function
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(3,8)
(2,4)
(1,2)
(-1,1/2)
(-2,1/4)
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y x
(0, 1)
(1, 0)
a gt 1
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Change exponential expression into an equivalent
logarithmic expression.
Change logarithmic expression into an equivalent
exponential expression.
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Domain of logarithmic function Range of
exponential function
Range of logarithmic function Domain of
exponential function
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y x
(0, 1)
(1, 0)
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y x
(0, 1)
(1, 0)
a gt 1
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Properties of the Graph of a Logarithmic Function
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 contains the points (1,0) and (a,1).
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The Natural Logarithm
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(e, 1)
(1, 0)
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(e3,1)
(4,0)
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The Common Logarithmic Functionbase 10
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Logarithmic Equations