College Algebra, 2013a

436 Exponential and Logarithmic Functions
71. f(x) =3 x+2 − 4
f −1 (x) =log 3 (x +4)− 2
6
5
4
3
2
1
y
−4−3−2−1 1 2 3 4 5 6
−1
−2
−3
−4
y = f(x) =3 x+2 − 4
y = f −1 (x) =log 3 (x +4)− 2
73. f(x) =−2 −x +1
f −1 (x) =− log 2 (1 − x)
x
72. f(x) =log 4 (x − 1)
f −1 (x) =4 x +1
6
5
4
3
2
1
y
−2 −1 1 2 3 4 5 6
−1
−2
y = f(x) =log 4 (x − 1)
y = f −1 (x) =4 x +1
74. f(x) = 5 log(x) − 2
f −1 (x) =10 x+2
5
x
2
1
y
−2 −1 1 2
−1
−2
y = f(x) =−2 −x +1
y = f −1 (x) =− log 2 (1 − x)
x
5
4
3
2
1
−4−3−2−1 1 2 3 4 5
−1
−2
−3
−4
y = f(x) =5log(x) − 2
y = f −1 (x) =10 x+2
5
y
x
75. (a) M(0.001) = log ( 0.001)
= log(1) = 0.
)
(b) M(80, 000) = log = log(80, 000, 000) ≈ 7.9.
(
80,000
0.001
76. (a) L(10 −6 ) = 60 decibels.
(b) I =10 −.5 ≈ 0.316 watts per square meter.
(c) Since L(1) = 120 decibels and L(100) = 140 decibels, a sound with intensity level 140
decibels has an intensity 100 times greater than a sound with intensity level 120 decibels.
77. (a) The pH of pure water is 7.
(b) If [H + ]=6.3 × 10 −13 then the solution has a pH of 12.2.
(c) [H + ]=10 −0.7 ≈ .1995 moles per liter.