Chapter 10 – Algebra 2 – Selected Answers ‘Evens’
p.1
Section 10.1 (p.457)
Oral Ex/ 1a. 3 b. 1/3 2a. 2 b. ½ 3a. 4 b. ¼ 4a. 2 b. ½ 5. 1/3 6. 9 7. 8 8. 1/5
9. c 10. a 11. c 12. a 13. b 14. a 15. b 16. a 17a. False b. True 18a. False b. True
19a. False b. True 20a. False b. True 21a. False b. True 22a. False b. True 23. 2
24. 3/2 25. –3 26. –4/3 27. Divide by 3; raise to the 4th power 28. Divide by 5; raise to
the –2/3 power 29. Raise to the –1/2 power; add 3 30. Raise to –2 power; divide by 5
Written Exercises
4
1
2. 3 4. ½ 6. 9 8. 1/125 10. –1/8 12. 27/8 14. –27 16. 1/49 18. 1/3 20. 8 22. p 3 q 3
24.
x2
y
4
3
or x 2 y
38. a2 40.
 43
26.
2b2
c
1
b
1
4
or b
 14
4
3
or 2b2c
 43
28.
q2
or p 1q 2 30. 4 32. 3 34.
p
6
32 36. 4 4 8
42. x – 2x2 44a. 1/36 b. 1/108 46a. 1/72 b. 27/8 48. 3 50. 4
Section 10.2 (p.461)
Oral Ex/ 1. 71.5 2. 5 3. 42 4. 6
11. –3/2 12. ¼
Written Exercises
2a. 7
3 2
b. 49
3
c. 7
6
d. 7
3
2
5. 9 6. 1 7. 7
2
8. 3
10
9. –2 10. 3/2
4. 5 6. 16 8. 1 10. 1 12. 2 14. 1/5 16. 3  2 2
3
18. 2 2 20. 3/2 22. –1/2 24. 11/4 26. –5/9 28. 3 30. 1 32. 0, 2
38. x = 0, 1
Section 10.3 (p.465)
Oral Ex/ 1a. 12 b. 3 c. –15 d. 3x + 3 2a. 13 b. 16 c. –17 d. 3x + 1
3a. 18 b. 38 c. 3x2 + 6 d. 9x2 + 2 4a. 12 b. 18 c. x2 + 3 d. x2 + 2x + 3
5. x/3 6. x – 1 7. Let h 1 or h 1 ( x) represent an inverse function. Then, since h(x) does
not pass the horizontal line test (is not 1-to-1), there is no inverse (function). Some texts
will let h 1 represent an inverse relation which may or may not be a function.
Chapter 10 – Algebra 2 – Selected Answers ‘Evens’
Section 10.3 (continued)
Written Exercises
2a. 1 b.  11
c. –3 d. 2x  3 4a. 4 b. 2 2 c. 22 x d. 4x 6a. 0 b. 4 3  3 c.
2
yes
no inverse (function)
x  3 d. x–6
y = 3x – 6
yes
f 1( x)  12x
p.2
g 1( x) 
x3
2
g 1 ( x)  3 x  2
x 3
2
24. f(x) = x2 is not ‘1-to-1’. It doesn’t pass the horizontal line test and therefore has no
inverse. g(x) = x is one-to-one. Note the Dg  x x  0  Rg 1 & Rg   y y  0  Dg 1
1
g ( x) 
5
To find the inverse of y = x , we interchange the x & y to get: x =
y and solve this
second equation for ‘y’ getting: g 1 ( x)  y  x 2 with the restriction that the domain of the
inverse function consists of only nonnegative numbers, x  0 . The graph is the right side
of the parabola.
Chapter 10 – Algebra 2 – Selected Answers ‘Evens’
Section 10.4 (p.470)
p.3
1
1 5. log 64 = 3 6. log 27 = 3/2
Oral Ex/ 1. 25 = 32 2. 32 = 9 3. 7 2  7 4. 34  81
4
9
7. log10 0.01 = –2 8. log16 18   34 9. 2 10. 4 11. 2 12. –2 13. 3/2 14. 0 15. 16 16. 5
17. 3; 4 18. 2; 3 19. –4; –3 20. –10, 10
Written Exercises
2. 2 4. 1 6. 2/3 8. –3 10. 5/2 12. 1/6 14. 2/5 16. –3 18. –3/2 20. 216 22. 36 6
24. 3 26. 2 28. 7 30. no solution 32a. 3; 1/3 b. ½ ; 2 c. For a, b > 0, not equal to 1:
1
34a. 4x b. 16; 1/8 c. Dg   positive numbers  Rg 1 & Rg  eals  Dg 1
log a b 
logb a
40. 8 42. negative
Section 10.5 (p.475)
Oral Ex/ 1. 4log 3 M 2. 6log3 N 3. 4log3 M  log3 N 4. log3 M  3log3 N
5.  log3 M 6. 12 log3 M 7. 23 log3 N 8.  32 log3 N 9. log a 12 10. loga 75 11. log a 16
12. log a 81 13. log a 6 14. log a 6 15. logb 30 16. log b 15 17. logb p 2q 18. log b
19. log b rs 20. logb
x
y
x
y3
21. c + d 22. 2c + d 23. c + 2d 24. c – d
Written Exercises
2. 4log 2 M  4log 2 N 4. 23 log2 M  13 log 2 N 6. 7log 2 M  7log 2 N 8.  log 2 M  log 2 N
10. 0.65 12. 0.48 14. 1.55 16. 2.95 18. –3.30 20. 2.20 22. log10
x
y4
26. log 5 25y x 28. log 9 3 x 30. 2 32. –2 34. 54 36. 3 38. 9 40. 5/2
42a. 3 3 b. undefined c. 0 44. 25 46. 16 48. 2 34 50. 3, 6
24. log 5 M 4 N
Chapter 10 – Algebra 2 – Selected Answers ‘Evens’
p.4
Section 10.6 (p.481)
Oral Ex/ 1. .6075 2. 1.6075 3. 2.6075 4. –.3925 5. .9222 6. 1.9222 7. –.0778
log 7
log8
log3
8. –1.0778 9. 4.05 10. 8.34 11. 83.4 12. .834 13.
14.
15.
log 2
log 9
2log8
log 7
16. 
log3
Written Exercises
2. 1.79  1010 4. 6460 6. 3.04 8. 55.4 10. 2.55 12. 40.3 14. .00123 16a. log1 5 b. 1.43
18a.
log 2
log1.02
b. 35.0 20a.
3
2 log12
b. 1.39 22a. 2 
log 21
log 4
b. –.196 24. 2/5 26. 13/9
28. 354 30. 83,900 32. 9.92  108 34. 135 36. 1.16 38. –.356 40. 1, 1.26
log c b
42. Change-of-Base Theorem - log a b 
log c a
Proof: We’ll use: aloga b  b Since log and exponent are inverse functions, f 1  f ( x)   x .
Begin with log c b and substitute for ‘b’ using the result above:.


Now use the ‘Down in front!’ Law log x y z  z log x y to move the exponent down.


logc b  logc aloga b   log a b  logc a   logc b   log a b  logc a  . Now divide by logc a
to get:
log c b
 log a b q.e.d.
log c a
Section 10.7 (p.486)
Oral Ex/ 1. 5(1.1)t, 40(1.05)t, $60, 7% 2. 10,000(.7)t, 300(.8)t, $250, 5%


3. 1000  2 9 , 3  106 2 25 , 7500, 12 years 4. 80  12  8 , 1200  12  30 , 500, 3
t
t
t
t
Problems
2a. $107.20 b. $141.57 c. $200.42 d. $401.69
4a. $1126.83 b. $1269.73 c. $1430.77 d. $3300.39
6a. $3150.00 b. $2066.72 c. $1220.37 d. $425.52 8a. 8N0 b. 236N0 c. 4.72  1021 N 0
10. 25 g 12. 18.9 or approximately 19 years 14. B 16. 4.64 min 18. 14.9% 20. 20.5%
22. 1.24 x 107
Chapter 10 – Algebra 2 – Selected Answers ‘Evens’
p.5
Section 10.8 (p.490)
Oral Ex/ 1. e1.39 = 4 2. e1.39  14 3. e1 = e 4. ln 7.39  2 5. ln.14  2 6. ln1.22  15
1
1
7. –1 8. 12 9. ½ 10. e5 11. e 3 12. ln 3 13. ¾ 14. 10 15. e 2 16. 2.718
Written Exercises
2. e4.61 = 100 4. e2  12 6. ln 1097 = 7 8. ln 1.40 = 1/3 10. 10 12. – ½ 14. undefined
e
16. 0.5 18. ln 4 20. ln 21 22. ln 16
24. e 2 26. e 28. e6 30. ln 13 32. ln 2 34. ln 17
3e
36. 12 ln5 38. ln 4 40. e, e 1 42.
1 5
44. D : x  0, R  eals
2
50a. e5 b. e2 c. e 2
46. D : x  0, R  eals
Chapter Review (p.496)
2. c 4. d 6. b 8. c 10. d 12. a 14. b 16. c
Chapter Test (p.497)
1a. 8 b. 4/3 2a. y 5 b. 125 3. 5 4a. 15 b. 4x2 – 4x + 5


5. f ( g ( x))  3 x3  1  1  3 x3  x and g ( f ( x)) 
6a. log2 8 = 3 b. 16
10.
 32

3

3
x 1 1  x 1 1  x
1 7a. 3 b. 3 2 8a. 4 b. 8 9a. .903 b. 1.079 c. 1.176
 64
log 2
11. 7.9 h 12.  e 4 13. ln
3log5
e
7
Mixed Problem Solving (p.498)
1
2. The equation 1   x has no real solution. 4. 120 rev/min 6. 10m x 20m
x
8. 2 eagles, 2 quarter-eagles; 1 eagle, 6 quarter-eagles; 10 quarter-eagles
10. 7, 8, 9, –6, –5, –4 12. 5.4 years
Preparing for College Entrance Exams
2. D 4. B 6. E 8. C