Title: Logarithmic Functions
1Logarithmic Functions
2One one Function
3(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
4The inverse of is the function
5(3,8)
(2,4)
(1,2)
(-1,1/2)
(-2,1/4)
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7y x
(0, 1)
(1, 0)
a gt 1
8Change exponential expression into an equivalent
logarithmic expression.
Change logarithmic expression into an equivalent
exponential expression.
9Domain of logarithmic function Range of
exponential function
Range of logarithmic function Domain of
exponential function
10y x
(0, 1)
(1, 0)
11y x
(0, 1)
(1, 0)
a gt 1
12Properties 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).
13The Natural Logarithm
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15(e, 1)
(1, 0)
16(e3,1)
(4,0)
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18The Common Logarithmic Functionbase 10
19Logarithmic Equations