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Section 4.2
8. Given: F(x) = 3x and G(x) = (1/4)x, what is G(-3)? G(-3) = (1/4)-3 = 64

14. Graph F(x) = 4x
X F(x)
0 1
1 4
2 16
-1 .25

58. 32t+1=161-t
3t+3 = 2-2t
5t = -1
T = -1/5

66. 1/81 = K-4
74. A= $45,000(1 + .035/12)12

Section 4.3
4. 25=32 therefore log232=5

14. X=log3(1/81), therefore 3x=1/81

16. logx(27/64) = 3
X3= 27/64 X = (27/64)

46. F(x) = log10X
X Y = log10X
1 0
2 .301
3 .477
4 .602
5 .699

62. log2 2 /5
Log22 + log2 -log25

72. logbK + logbM - logbA
Logb (K*M/A)

82. Given: log102 = .3010; log103 = .4771
Log1012 = log102 + log103 + log102
Log1012 = .3010 +.4771 + .3010

Section 4.4
14. log.078 = -1.108 (used calculator)

30. Limes, 1.6*10-2 , ph=-log[1.6*10-2]
Ph = -log 1.6 - log10-2
Ph = -log1.6 +2
Ph = 1.80

a. F(t) = 74.61 +3.84ln(t)
74.61 +3.84 ln (8)
F(t) = 82.59, function is very accurate
b. As the percentage increases towards 100% the rate of kids that volunteer will slow and a large number of years will be needed to continue to approach 100% representative of a logarithmic function. An exponential function would reach 100% in a few years, which is not representative of the rate at which the kids are volunteering.
Section 4.5
6. 5x=13
X = ln13/ln5 = 1.59

24. 5(1.2)3x-2 + 1 = 7
(3x-2)ln1.2 = ln6/5
3x-2 = ln(6/5)/ln1.2
3x = [ln(6/5)/ln1.2] +2
X = [[ln(6/5)/ln1.2] +2]/3

60. R=p-kln(t) r-p=-kln(t) p-r=kln(t)
(p-r)/k = ln(t) e[(p-r)/k]=t 76. 20,000=16,000(1+r/4)5.25*4
Ln1.25 = 21ln(1+r/4)
Ln1.25/21 =ln(1+r/4)
1.0107 = 1+r/4
r=.04, therefore rate =40%

94. (ex)2-4ex+3 = (ex-3)(ex-1)

Section 4.6
2. Given: y=2e.2x
A. 3 mil = 2e.2x
1.5mil = e.2x
Ln1.5 = .2x
X=ln1.5/.2 = 2.03 years
B. 2e.2x=6

10. M=1 M=3
1=6-5/2logx 3=6-5/2logx
5=5/2logx 3=5/2logx
10=5logx 6=5logx
2=logx 6/5=logx
X=100 X=15.8
Ratio; 100:16 or 25:4

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