12.6: Exponential and Logarithmic Functions- Answers to the Homework Exercises
( \newcommand{\kernel}{\mathrm{null}\,}\)
Inverse Functions
- yes
- yes
- no; [−2,0] or [0,2]
- yes
- no
- no
- yes
- no
- g−1(x)=4−2xx
- f−1(x)=−5x+10
- f−1(x)=3√x+3
- f−1(x)=−x−1x−1
- g−1(x)=−x+15
- h−1(x)=(−2x+4)34
- f−1(x)=2x+7x+3
- g−1(x)=(x−2)3−1
- g−1(x)=3x−9
- f−1(x)=−4x+123
- f−1(x)=−3x−3x+2
- g−1(x)=−3x+2
- f−1(x)=5√−x+32
- f−1(x)=−1−xx
- g−1(x)=−3x+12
Exponential Functions
-
Figure 12.6.1
-
Figure 12.6.2
-
Figure 12.6.3
-
Figure 12.6.4
- 0
- −34
- −23
- −2
- No Solution
- No Solution
- No Solution
- 0
- 13
- 38
- −1
- −54
- 0
- −56
- −43
- 0
- 14
- No Solution
- 23
- −1
Logarithmic Functions
- 92=81
- 132=169
- 162=256
- log81=0
- log642=16
- log14412=12
- 13
- 2
- 6
- 0
- 12
- (−107,∞)
- (−∞,78)
-
Figure 12.6.5
-
Figure 12.6.6
-
Figure 12.6.7
- 5
- 121
- −1253
- −12
- 25
- 1,000
- 4511
- −24013
- 283243
Logarithm Properties
- loga(mk6n)
- log86x
- log8(6x3−12)
- loga(a2(2x+1)3(2x−1)2)
- 3−12log4(x−1)
- 2log2x−6log2y
- logbx+3logbz
- logbx+5logby−7logbz
- 2.8540
- −3.2694
- 1.3778
- 1
- 0.394
- √5
- 0
Solve Exponential and Logarithmic Functions
- 377124
- 10
- 6
- 8
- 9
- No Solution
- 115
- −7+log37; −5.2288
- 18log23.6; 0.2310
- log21110; 0.1375
- 19log539.2; 0.2533
- 24.75 years
- year 2034
- 105 days
- 10.5 minutes