4.3 Logarithmic Function (basic)

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4.3 Logarithmic Function (basic)
4.4 Logarithmic Transformations
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The Family of Logarithmic Functionsa gt 1
as x?8, loga(x)? 8 as x?0, loga(x)? -8
f(x) loga(x) with a gt 1 domain positive
reals range reals VA y 0 x intercept 1
PRACTICE 25/194, 27/194, 31/195, 33/195,
37a,d/195
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Transformations of the Logarithm Functions
25a/194 sketch the graph of f(x) ln(x2)
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Transformations of the Logarithm Functions
25b/194 sketch the graph of f(x) ln(2x)
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Transformations of the Logarithm Functions
25c/194 sketch the graph of f(x) -2ln(x)
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Recognizing Logarithm Functions
27
29
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Recognizing Logarithm Functions
X Y
1/9 -4
1/3 -3
1 -2
3 -1
9 0
27 1
81 2
31
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33/194 Given f(x) ln(12x), find f -1(x).
35/194 Given h(x) 3e(-0.2)x, find h -1(x).
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FIVE Properties of Logarithms
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POWER of Logarithms
Logarithms can be used to solve for unknown
variables that appear in the exponent!!
ek 4 Using graph and trial/errork 1.4, ek
4.0552 k 1.39, ek 4.0149 k 1.388, ek
4.0068k 1.387, ek 4.0028k 1.3865, ek
4.0008k 1.3863, ek 4.0000 So f(x)
100e1.3863t
ek 4 ln(ek) ln(4) k ln(4) 1.3863 So
f(x) 100e1.3863t
PRACTICE 43/195
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In Context
p182 The population of Vietnam in the year 2000
was approximately 79 million persons and was
growing at the rate of roughly 3.3 percent per
year. At that pace, in what year will the
population reach 100 million?
p183 Suppose one investment of 1500 grows at
5 per year while another investment of 1000
grows at 7 per year. When will the second
investment catch up to the first investment?
p184 The city of Atlanta and surrounding
urbanized areas experienced rapid growth during
the late twentieth century. The region had 1.86
million people in 1990 and 2.40 million in 1997.
Find a base-e population model.
CYU/185
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HW pages 195 196 25-46, 53-57 TURN IN 28,
32, 34, 36, 46, 54a,b