section 5.4 logarithmic functions
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Section 5.4 Logarithmic Functions. (a) 3 raised to what power yields 81?. (b) 2 raised to what power yields ?. Natural Logarithm Function. The range of f is all real numbers and the vertical asymptote is x = 2. - PowerPoint PPT PresentationTRANSCRIPT
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Section 5.4Logarithmic Functions
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3 21a log 81 b log8
(a) 3 raised to what power yields 81? 3log 813 81yy
43 3
4
y
y 3Therefore, log 81 4
32 23
y
y
2
1Therefore, log 38
(b) 2 raised to what power yields ?18
2
33
1log8
1 12 28 2
y
y
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3 2
2
3a log 2 b log1
c log 1
xf x x F xx
h x x
a The domain of consists of all for which 2 0.f x x
2 or 2,x
3b The domain of is restricted to 01
xFx
, 3 1, .
c Since the absolute value function is never negative, the domain would consist of all real numbers except 1 0.x
,1 1,
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Natural Logarithm Function
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2 3 so 5.x x
The domain of is 2, .f
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The range of f is all real numbers and the vertical asymptote is x = 2.
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ln 2f x x
The inverse implicitly is ln 2x y
2xe y
ln 2x y
12xe y f x
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Since the range of f equals the domain of f -1, the range of f is all real numbers.
1 2xf x e
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Common Logarithm Function
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2Solve: log 2 1 3 log 343 3xa x b
2(a) Change log 2 1 3 to exponential form.x
32 2 1x 8 2 1x 72
x
2 27log 2 1 log 8 32
(b) Change log 343 3 to exponential form.x
3 343x 7x
7log 343 3
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3Solve: 2 6xe
3 3xe Isolate the exponential.
ln 3 3x Change to logarithmic form.
ln 33
x Exact solution
0.366 Approximate solution
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