Chapter 5 AnswersSection 5 – 0

1.

�

x1/2! 2.

�

y1 3! 3.

�

x1 4 ! 4.

�

x2/3! 5.

�

x3 4 ! 6.!

�

y4 5

7.

�

x7/2! 8.

�

x4 2 = x2 ! 9.

�

x3 6 = x1/2 ! 10.

�

x ! 11.

�

y4 ! 12.

�

x34

13.

�

y35 ! 14.

�

x45 ! 15.

�

x23 ! 16.

�

8x5y7 ! 17.

�

−10x6y5! 18.

�

−2x7y6

19.

�

x2! 20.

�

x2 3! 21.

�

y7 6! 22.

�

x3! 23.

�

x 5 4 ! 24.

�

x1 4

25.

�

x17/12! 26.

�

x7 6 ! 27.

�

x7 12 ! 28.

�

x + x7/6! 29.

�

x13/12 + x !

30.

�

16x6y8 ! 31.

�

8x9y12! 32.

�

−27x3y3! 33.

�

x4! 34.

�

x3! 35.

�

y2

36.

�

x1/3 = x3 ! 37.

�

x ! 38.

�

x1/6! 39.

�

y3

x2! 40.

�

x4y ! 41.

�

y4

x5

42.

�

1x3y4

! 43.

�

y2

x3! 44.

�

x4

9! 45.

�

−5y4

2x! 46.

�

−12x4y3

! 47.

�

−3y8

2x6

48.

�

4y7

5x4! 49.

�

y ! 50.

�

1x2! 51.

�

−12x2

! 52.

�

1x2! 53.

�

x 3

54.

�

x9/2! 55.

�

x1/12! 56.

�

1x1/6

! 57. 4! 58. 9! 59.

�

75!

60.

�

1112 ! 61. 3! 62. 5! 63.

�

23

! 64.

�

−54! 65.

�

43!

66. 3! 67. 27! 68. 4! 69. 32! 70.

�

827! 71.

�

49

72.

�

64125

! 73.

�

169! 74.

�

13! 75.

�

19

! 76.

�

12! 77. 3

78.

�

97! 79.

�

52! 80.

�

43! 81.

�

1125

! 82.

�

19! 83.

�

164!

84.

�

14! 85.

�

254 ! 86.

�

827! 87.

�

94

! 88.

�

64125

! 89.

�

169

90.

�

125216

! 91.

�

27125

! 92.

�

925

Math 370 Chapter 5 Answers! Page 1 of 15! © 2018 Eitel

Section 5 – 1

1.

�

x = 4 ! 2.

�

x = 3! 3.

�

x = 1! 4.

�

x = 4! 5.

�

x =1 ! 6.

�

x = 0

7.

�

ARN ! 8. x = −45! 9.

�

x = −3! 10.

�

x = 2! 11.

�

x =13! 12.

�

x = 6

13.

�

x =43! 14.

�

x = 0! 15.

�

x =53! 16.

�

x =52 ! 17.

�

x =23! 18.

�

x = −23

19.

�

x =23 ! 20.

�

x =32 ! 21.

�

x =32! 22.

�

x =25! 23.

�

x =75! 24.

�

x =32

25.

�

x = 2! 26.

�

x = 3! 27.

�

x = 4! 28.

�

x =13! 29.

�

x =14 ! 30.

�

x =13

31.

�

x =34! 32.

�

x = 1! 33.

�

x =43! 34.

�

x = 1! 35. x = 9 ! 36.

�

x = −4

37.

�

x = −2 ! 38.

�

x = −3! 39.

�

x =13! 40.

�

x =12! 41.

�

x =−13

! 42.

�

x =−43

43.

�

x =−23! 44.

�

x =−23! 45.

�

x =−34! 46.

�

x =−13! 47.

�

x = −5 ! 48.

�

x = −2

Math 370 Chapter 5 Answers! Page 2 of 15! © 2018 Eitel

Section 5 – 2: Graphs of the Exponent Function!

1)

�

y = 2x ! 2)

�

y = 3x ! 3)

�

y = 4 x+1

Hor. Asp. y = 0! Hor. Asp. y = 0! Hor. Asp. y = 0Domain:

�

x ∈ −∞,+∞( ) or ℜ ! Domain:

�

x ∈ −∞,+∞( ) or ℜ ! Domain:

�

x ∈ −∞,+∞( ) or ℜ

Range:

�

y ∈ 0,+∞( ) or ℜ+ ! Range:

�

y ∈ 0,+∞( ) or ℜ+ ! Range:

�

y ∈ 0,+∞( ) or ℜ+

4)

�

y = 2x −1! 5)

�

y = 3x−2! 6)

�

y = −2x

Hor. Asp. y = –1! Hor. Asp. y = 0! Hor. Asp. y = 0Domain:

�

x ∈ −∞,+∞( ) or ℜ ! Domain:

�

x ∈ −∞,+∞( ) or ℜ ! Domain:

�

x ∈ −∞,+∞( ) or ℜ

Range:

�

y ∈ −1,+∞( ) ! Range:

�

y ∈ 0,+∞( ) or ℜ+ ! Range:

�

y ∈ −∞,0( ) or ℜ−

7)

�

y = 4−x ! 8)

�

y = 5x − 3! 9)

�

y = 4 x + 2

Hor. Asp. y = 0! Hor. Asp. y = –3! Hor. Asp. y = 2 Domain:

�

x ∈ −∞,+∞( ) or ℜ ! Domain:

�

x ∈ −∞,+∞( ) or ℜ ! Domain:

�

x ∈ −∞,+∞( ) or ℜ

Range:

�

y ∈ 0,+∞( ) or ℜ+ ! Range:

�

y ∈ −3,+∞( ) ! Range:

�

y ∈ 2,+∞( )

Math 370 Chapter 5 Answers! Page 3 of 15! © 2018 Eitel

10)

�

y = 3x+2! 11)

�

y = 4 x +1! 12)

�

y = 3x − 2

Hor. Asp. y = 0! Hor. Asp. y = 1! Hor. Asp. y = – 2 Domain:

�

x ∈ −∞,+∞( ) or ℜ ! Domain:

�

x ∈ −∞,+∞( ) or ℜ ! Domain:

�

x ∈ −∞,+∞( ) or ℜ

Range:

�

y ∈ 0,+∞( ) or ℜ+ ! Range:

�

y ∈ 1,+∞( ) ! Range:

�

y ∈ −2,+∞( )

13)

�

y = 1 2( )x ! 14)

�

y = (1 3)x ! 15)

�

y = (1 3)x−2

Hor. Asp. y = 0! Hor. Asp. y = 0! Hor. Asp. y = 0 Domain:

�

x ∈ −∞,+∞( ) or ℜ ! Domain:

�

x ∈ −∞,+∞( ) or ℜ ! Domain:

�

x ∈ −∞,+∞( ) or ℜ

Range:

�

y ∈ 0,+∞( ) or ℜ+ ! Range:

�

y ∈ 0,+∞( ) or ℜ+ ! Range:

�

y ∈ 0,+∞( ) or ℜ+

16

�

y = (1 4)x + 2 ! 17)

�

y = (1 3)x −1! 18)

�

y = − 1 2( )x

Hor. Asp. y = 2! Hor. Asp. y = –1! Hor. Asp. y = 0 Domain:

�

x ∈ −∞,+∞( ) or ℜ ! Domain:

�

x ∈ −∞,+∞( ) or ℜ ! Domain:

�

x ∈ −∞,+∞( ) or ℜ

Range:

�

y ∈ 2,+∞( ) ! Range:

�

y ∈ −1,+∞( ) ! Range:

�

y ∈ −∞,0( ) or ℜ−

Math 370 Chapter 5 Answers! Page 4 of 15! © 2018 Eitel

19)

�

y = 1 2( )x+3! 20

�

y = 1 3( )−x ! 21)

�

y = 1 2( )x − 2Hor. Asp. y = 0! Hor. Asp. y = 0! Hor. Asp. y = –2 Domain:

�

x ∈ −∞,+∞( ) or ℜ ! Domain:

�

x ∈ −∞,+∞( ) or ℜ ! Domain:

�

x ∈ −∞,+∞( ) or ℜ

Range:

�

y ∈ 0,+∞( ) or ℜ! Range:

�

y ∈ 0,+∞( ) or ℜ! Range:

�

y ∈ −2,∞( )

22)

�

y = 1 3( )x + 4 ! 23)

�

y = (1 2)x−3 ! 24)

�

y = (1 4)x+1

Hor. Asp. y = 4! Hor. Asp. y = 0! Hor. Asp. y = 0 Domain:

�

x ∈ −∞,+∞( ) or ℜ ! Domain:

�

x ∈ −∞,+∞( ) or ℜ ! Domain:

�

x ∈ −∞,+∞( ) or ℜ

Range:

�

y ∈ 4,+∞( ) ! Range:

�

y ∈ 0,+∞( ) or ℜ+ ! Range:

�

y ∈ 0,+∞( ) or ℜ+

25)

�

y = − 3 4( )x ! 26)

�

y = 3x +1! 27)

�

y = − 1 2( )−x

Hor. Asp. y = 0! Hor. Asp. y = 1! Hor. Asp. y = 0 Domain:

�

x ∈ −∞,+∞( ) or ℜ ! Domain:

�

x ∈ −∞,+∞( ) or ℜ ! Domain:

�

x ∈ −∞,+∞( ) or ℜ

Range:

�

y ∈ −∞,0( ) or ℜ− ! Range:

�

y ∈ 1,+∞( ) ! Range:

�

y ∈ −∞,0( ) or ℜ−

Math 370 Chapter 5 Answers! Page 5 of 15! © 2018 Eitel

28)

�

y = 3x+1! 29)

�

y = (1 2)x−3 ! 30)

�

y = 2x − 3

Hor. Asp. y = 0! Hor. Asp. y = 0! Hor. Asp. y = –3 Domain:

�

x ∈ −∞,+∞( ) or ℜ ! Domain:

�

x ∈ −∞,+∞( ) or ℜ ! Domain:

�

x ∈ −∞,+∞( ) or ℜ

Range:

�

y ∈ 0,+∞( ) or ℜ+ ! Range:

�

y ∈ 0,+∞( ) or ℜ+ ! Range:

�

y ∈ −3,+∞( )

31)

�

y = 4 5( )x −1! 32)

�

y = (3 2)x+3 ! 33)

�

y = − 5 2( )x

Hor. Asp. y = –1! Hor. Asp. y = 0! Hor. Asp. y = –1 Domain:

�

x ∈ −∞,+∞( ) or ℜ ! Domain:

�

x ∈ −∞,+∞( ) or ℜ ! Domain:

�

x ∈ −∞,+∞( ) or ℜ

Range:

�

y ∈ −1,+∞( )! Range:

�

y ∈ 0,+∞( ) or ℜ+ ! Range:

�

y ∈ −∞,0( ) or ℜ−

34)

�

y = 4 x + 2! 35)

�

y = 3x−1! 36)

�

y = (1 3)x + 3

Hor. Asp. y = 2! Hor. Asp. y = 0! Hor. Asp. y = 3 Domain:

�

x ∈ −∞,+∞( ) or ℜ ! Domain:

�

x ∈ −∞,+∞( ) or ℜ ! Domain:

�

x ∈ −∞,+∞( ) or ℜ

Range:

�

y ∈ 2,+∞( ) ! Range:

�

y ∈ 0,+∞( ) or ℜ+ ! Range:

�

y ∈ 3,+∞( )

Math 370 Chapter 5 Answers! Page 6 of 15! © 2018 Eitel

Section 5 – 3

1.

�

x = 4y ! 2.

�

10x = 3! 3.

�

5x = y ! 4.

�

1 2( )x = y ! 5.

�

6 = ex !

6

�

y =10x ! 7.

�

x 5 = y + 2! 8.

�

x 1 2( ) = y ! 9.

�

y 1 3( ) = x ! 10.

�

x = 8

11.

�

x = 27! 12.

�

x =1 9 ! 13.

�

x =1! 14.

�

x =1 10 = .1! 15.

�

x =1 100 = .01

16.

�

4 = x ! 17.

�

64 = x ! 18.

�

132 = x ! 19.

�

127 = x ! 20.

�

x = 3!

21.

�

x =32! 22.

�

x =52! 23.

�

x =23 ! 24.

�

x =12

! 25.

�

x =34

!

26.

�

x = −4 ! 27.

�

x = −5 ! 28.

�

x = −1! 29.

�

x = 0! 30.

�

x = 3

31.

�

x = 4! 32.

�

x =1! 33.

�

x = 49! 34.

�

x = 8! 35.

�

x =125!

36.

�

x =916! 37.

�

x = 125! 38.

�

x =13! 39.

�

x = 8 ! 40.

�

x = 8

41.

�

x = −2! 42.

�

x =278! 43. 1! 44. 2! 45. 4

46. 0! 47. –1! 48. –2! 49. –3! 50. –251. 1/ 2! 52. 1! 53. 3! 54. 0!

Math 370 Chapter 5 Answers! Page 7 of 15! © 2018 Eitel

Section 5 – 4: Graphs of the Logarithmic Function!

1)

�

y = log2 x ! 2)

�

y = log3 x ! 3)

�

y = log3(x +1)

Vert. Asp. x = 0! Vert. Asp. x = 0! Vert. Asp. x = –1 Domain:

�

x ∈ 0,+∞( ) or ℜ+ ! Domain:

�

x ∈ 0,+∞( ) or ℜ+ ! Domain:

�

x ∈ −1,+∞( )

Range:

�

y ∈ −∞,+∞( ) or ℜ ! Range:

�

y ∈ −∞,+∞( ) or ℜ ! Range:

�

y ∈ −∞,+∞( ) or ℜ

4)

�

y = log3(x − 2) ! 5)

�

y = log3(x + 2)! 6)

�

y = −log2 x

Vert. Asp. x = 2! Vert. Asp. x = –2! Vert. Asp. x = 0 Domain:

�

x ∈ 2,+∞( ) ! Domain:

�

x ∈ −2,+∞( ) ! Domain:

�

x ∈ 0,+∞( ) or ℜ+

Range:

�

y ∈ −∞,+∞( ) or ℜ ! Range:

�

y ∈ −∞,+∞( ) or ℜ ! Range:

�

y ∈ −∞,+∞( ) or ℜ

7)

�

y = log4 (−x) ! 8)

�

y = ln x ! 9)

�

y = log(x + 3)

Vert. Asp. x = 0! Vert. Asp. x = 0! Vert. Asp. x = –3 Domain:

�

x ∈ −∞,0( ) or ℜ− ! Domain:

�

x ∈ 0,+∞( ) or ℜ+ ! Domain:

�

x ∈ −3,+∞( )Range:

�

y ∈ −∞,+∞( ) or ℜ ! Range:

�

y ∈ −∞,+∞( ) or ℜ ! Range:

�

y ∈ −∞,+∞( ) or ℜ

Math 370 Chapter 5 Answers! Page 8 of 15! © 2018 Eitel

10)

�

y = log2(x −1) ! 11)

�

y = log3(x) −1 ! 12)

�

y = log3(x) + 2

Vert. Asp. x = 1! Vert. Asp. x = 0! Vert. Asp. x = 0 Domain:

�

x ∈ 1,+∞( ) ! Domain:

�

x ∈ 0,+∞( ) or ℜ+ ! Domain:

�

x ∈ 0,+∞( ) or ℜ+

Range:

�

y ∈ −∞,+∞( ) or ℜ ! Range:

�

y ∈ −∞,+∞( ) or ℜ ! Range:

�

y ∈ −∞,+∞( ) or ℜ

13)

�

y = log1 2 x ! 14)

�

y = log1 3 x ! 15)

�

y = log1 3(x − 2)

Vert. Asp. x = 0! Vert. Asp. x = 0! Vert. Asp. x = 2 Domain:

�

x ∈ 0,+∞( ) or ℜ+ ! Domain:

�

x ∈ 0,+∞( ) or ℜ+ ! Domain:

�

x ∈ 2,+∞( )

Range:

�

y ∈ −∞,+∞( ) or ℜ ! Range:

�

y ∈ −∞,+∞( ) or ℜ ! Range:

�

y ∈ −∞,+∞( ) or ℜ

16)

�

y = log2 3(x −1)! 17)

�

y = log1 2(−x)! 18)

�

y = log3 5(x +1)

Vert. Asp. x = 1! Vert. Asp. x = 0! Vert. Asp. x = –1 Domain:

�

x ∈ 1,+∞( ) ! Domain:

�

x ∈ −∞,0( ) or ℜ− ! Domain:

�

x ∈ −1,+∞( )

Range:

�

y ∈ −∞,+∞( ) or ℜ ! Range:

�

y ∈ −∞,+∞( ) or ℜ ! Range:

�

y ∈ −∞,+∞( ) or ℜ

Math 370 Chapter 5 Answers! Page 9 of 15! © 2018 Eitel

19)

�

y = log1 5 (x − 4) ! 20

�

y = log3 5(−x) ! 21)

�

y = log2 3(x + 2)

Vert. Asp. x = 4! Vert. Asp. x = 0! Vert. Asp. x = –2Domain:

�

x ∈ 4,+∞( ) ! Domain:

�

x ∈ −∞,0( ) or ℜ− ! Domain:

�

x ∈ −2,+∞( )

Range:

�

y ∈ −∞,+∞( ) or ℜ ! Range:

�

y ∈ −∞,+∞( ) or ℜ ! Range:

�

y ∈ −∞,+∞( ) or ℜ

22)

�

y = −log1 2(−x) ! 23)

�

y = log3 4 x −1! 24)

�

y = log5 6 x + 2

Vert. Asp. x = 0! Vert. Asp. x = 0! Vert. Asp. x = 0 Domain:

�

x ∈ −∞,0( ) or ℜ− ! Domain:

�

x ∈ 0,+∞( ) or ℜ+ ! Domain:

�

x ∈ 0,+∞( ) or ℜ+

Range:

�

y ∈ −∞,+∞( ) or ℜ ! Range:

�

y ∈ −∞,+∞( ) or ℜ ! Range:

�

y ∈ −∞,+∞( ) or ℜ

25)

�

y = log1/2(−x) ! 26)

�

y = log2(x − 3) ! 27)

�

y = − log3 4 (−x)

Vert. Asp. x = 0! Vert. Asp. x = 3! Vert. Asp. x = 0 Domain:

�

x ∈ −∞,0( ) or ℜ− ! Domain:

�

x ∈ 3,+∞( ) ! Domain:

�

x ∈ −∞,0( ) or ℜ−

Range:

�

y ∈ −∞,+∞( ) or ℜ ! Range:

�

y ∈ −∞,+∞( ) or ℜ ! Range:

�

y ∈ −∞,+∞( ) or ℜ

Math 370 Chapter 5 Answers! Page 10 of 15! © 2018 Eitel

28)

�

y = log2(x + 4) ! 29)

�

y = log1 2(x − 3) ! 30)

�

y = log1 2(x +1)

Vert. Asp. x = –4! Vert. Asp. x = 3! Vert. Asp. x = –1 Domain:

�

x ∈ −4,+∞( ) ! Domain:

�

x ∈ 3,+∞( ) ! Domain:

�

x ∈ −1,+∞( )

Range:

�

y ∈ −∞,+∞( ) or ℜ ! Range:

�

y ∈ −∞,+∞( ) or ℜ ! Range:

�

y ∈ −∞,+∞( ) or ℜ

31)

�

y = −log2(−x) ! 32)

�

y = log4 (x − 2) ! 33)

�

y = − logπ xVert. Asp. x = 0! Vert. Asp. x = 2! Vert. Asp. x = 0

Domain:

�

x ∈ −∞,0( ) or ℜ−! Domain:

�

x ∈ 2,+∞( ) ! Domain:

�

x ∈ 0,+∞( ) or ℜ+

Range:

�

y ∈ −∞,+∞( ) or ℜ ! Range:

�

y ∈ −∞,+∞( ) or ℜ ! Range:

�

y ∈ −∞,+∞( ) or ℜ

34)

�

y = log2 x − 2 ! 35)

�

y = log3 x + 2 ! 36)

�

y = log1 3 x +1

Vert. Asp. x = 0! Vert. Asp. x = 0! Vert. Asp. x = 0 Domain:

�

x ∈ 0,+∞( ) or ℜ+ ! Domain:

�

x ∈ 0,+∞( ) or ℜ+ ! Domain:

�

x ∈ 0,+∞( ) or ℜ+

Range:

�

y ∈ −∞,+∞( ) or ℜ ! Range:

�

y ∈ −∞,+∞( ) or ℜ ! Range:

�

y ∈ −∞,+∞( ) or ℜ

Math 370 Chapter 5 Answers! Page 11 of 15! © 2018 Eitel

Section 5 – 51.

�

log2 5 + log2 x ! 2.

�

log3 x + log3 y ! 3.

�

2log2 3 + log2 x + log2 y ! 4.

�

ln x + 3ln y !

5.

�

2log x + 3log y ! 6.

�

4 + log3 x + 2log3 y ! 7.

�

13log4 x ! 8.

�

log x +12log y

9.

�

4 log5 x − 2log5 y ! 10.

�

2log x − 3log y ! 11.

�

log2 a + 3log2 x − 4 log2 y

12.

�

12log y − 1

3log x ! 13.

�

log3 x4y ! 14.

�

log5 x3y2! 15.

�

log8y5! !

16.

�

log4 25x3! 17.

�

log564x2 ! 18.

�

log2(6x −15) ! 19.

�

log5 24 x + 32( )

20.

�

log x2 − 3x( ) ! 21.

�

log3(18x − 27) ! 22.

�

log3 x4 + 4 x3( ) ! 23.

�

log4 2x4 − x3( )

24.

�

log4 3x2 − 6x( ) ! 25.

�

log x 2 − 2x − 3( ) ! 26.

�

log7 x2 − 4( ) ! 27.

�

log4 x 2 − 7x +10( )28.

�

log 3x2 − x − 2( )! 29.

�

log4 6x2 + 7x + 2( )! 30.

�

log5 8x2 −10x + 3( )! 31.

�

log 16x2

⎛ ⎝ ⎜

⎞ ⎠ ⎟

32.

�

log x2

y3⎛

⎝ ⎜ ⎞

⎠ ⎟ ! 33.

�

log5x4

x − 3⎛

⎝ ⎜ ⎞

⎠ ⎟ ! 34.

�

log32x −1x2

⎛ ⎝ ⎜

⎞ ⎠ ⎟ ! 35.

�

log28

3x − 4⎛ ⎝

⎞ ⎠

36.

�

log41

x + 3⎛ ⎝

⎞ ⎠ ! 37.

�

log x8

⎛ ⎝ ⎜

⎞ ⎠ ⎟ ! 38

�

log3x − 3x

⎛ ⎝ ⎜

⎞ ⎠ ⎟ ! 39.

�

log3x −13

9⎛

⎝ ⎜ ⎞

⎠ ⎟

40.

�

x ∈ 52

, + ∞⎛ ⎝

⎞ ⎠ ! 41.

�

x ∈ −∞ , 37

⎛ ⎝

⎞ ⎠ ! 42.

�

x ∈ 212

, + ∞⎛ ⎝

⎞ ⎠ ! 43.

�

x ∈ 0 , + ∞( )

44.

�

x ∈ℜ | x ≠ 0 or

�

x ∈ −∞ , 0( ) ∪ 0 , + ∞( ) ! 45.

�

x ∈ 0 , + ∞( ) ! 46. !

�

x ∈ 1 ,+∞[ )

47.

�

x ∈ 0 , 1( ) ∪ 1 , + ∞( ) ! ! 48.

�

x ∈ 1 , + ∞( ) ! 49.

�

x ∈ℜ | x ≠ 0

50.

�

x ∈ −3 , + ∞( ) ! 51.

�

x ∈ −4 , + ∞( ) ! 52.

�

x ∈ 2 , + ∞( )

53.

�

x ∈ 3 , + ∞( ) ! 54.

�

x ∈ −∞ , − 4( ) !

55.

�

f −1(x) = 3x ! 56.

�

f −1(x) = 6x ! 57.

�

f −1(x) = 10x ! 58.

�

f −1(x) = ex

59.

�

f −1(x) = 6x −1! 60.

�

f −1(x) = 10x−1! 61.

�

f −1(x) = log3 x ! 62.

�

f −1(x) = log5 x

63.

�

f −1(x) = log x ! 64.

�

f −1(x) = ln x ! 65.

�

f −1(x) = ln(x) −1! 66.

�

f −1(x) = ln(x −1)

Math 370 Chapter 5 Answers! Page 12 of 15! © 2018 Eitel

Section 5 – 61.

�

x = 6! 2.

�

x = −2 ! 3.

�

x = 3 or − 3! 4.

�

x = 5 or − 3!

5.

�

x = 5 or − 4 ! 6.

�

x =−12

or 13! 7.

�

x = −2 or 3! 8.

�

x =−12

or 4

9.

�

x = 4! 10.

�

x = 15! 11.

�

x = −6! 12.

�

x = 8!

13.

�

x = 7! 14.

�

x = 5! 15.

�

x = 7 or − 7! 16.

�

x = −5 or 3

17.

�

x = 5! 18.

�

x = 2! 19. x = 1 (not –16)! 20. x = 9 (not –3)

21. x = 3 (not –1/ 2)! 22. x = 4( not – 2/ 3)! 23. x = 5 (not – 4)! 24. x = 5/ 2 (not –5/ 2)

25. x = –2! 26.

�

x = 8! 27. No Solution (not –5)! 28.

�

x = 5

29. No Solution (not 0)!30.

�

x = 2! 31. x = 7! 32. x = 2

33. x = 4! 34. x = 10! 35. No Solution (not –2)! 36. x = 4

37. x = 1 (not –4)! 38. x = 2 (not –6)! 39. x = 2/ 3 (not –4)! 40.x = 1/ 4 or –3/ 2

41. x = 9 (not –2)! 42. x = 5

Section 5 – 7

1. .64! 2. –1.17! 3. .44! 4. 2.76! 5. .35! 6. 31.50

7. 1.02! 8. .09 ! 9. 4.11! 10. 2.54! 11. 1.82! 12. –5.40

13. .45! 14. –2.22! 15. 2.75! 16. .77! 17. 5011.87! 18. .04

19. 3.7! 20. .76! 21. 8! 22. 1! 23. 10! 24. !5

25. 281.84! 26. .01! 27.

�

.99 28. 10.38! 29. .05! 30. .63!

31. pH = 1.03! 32. pH = 6.39! 33.

�

2.51×10−4 mol / L ! 34.

�

7.94 ×10−7 mol / L

35.

�

x = 2.05! 36.

�

x = 1.56! 37.

�

x = .81! 38.

�

x = 1.40!

39.

�

x = .55! 40.

�

x = 1.41! 41.

�

x =1.65! 42. x = 3.92

43.

�

x = 1.45! 44.

�

x = 2.08! 45.

�

x = 1.10! 46.

�

x = 1.04 !

47. 332.78 or 332 penguins! 48. 6.13 years! 49. 8.03 years! 50. 4.55 years! !51. 7.81 grams! 52. 233.99 years! 53. 646.24 years

54. $ 19,740.13! 55. $ 16, 235.36! 56. 11.68 years!

57. 36.88 years! 58. 7.85 years! ! 59. $ 452.89Math 370 Chapter 5 Answers! Page 13 of 15! © 2018 Eitel

Chapter 5 Review Answers

1.

�

x = 5! 2.

�

x = 2! 3.

�

x = −2 ! 4.

�

x = −3! 5.

�

x = −4 !

6.

�

x = −2 ! 7.

�

x = 4 y−1 ! 8.

�

x3 = y ! 9.

�

y = ex−1 ! 10.

�

x = 11!

11.

�

x = 7! 12.

�

x = 14 ! 13. x = –4 ! 14. x = 1/ 10! 15. x = 9

16. x = 4! 17. x = 3 ! 18. x = 125 ! 19. x = –5! 20. x = 9

21. x = 5! 22. 4! 23. –2! 24. 5! 25. 2

26. –2! 27. 1 ! 28.

�

log5x8

⎛ ⎝ ⎜

⎞ ⎠ ⎟ ! 29.

�

log 9x − 36( )! 30.

�

log58x2

x − 4⎛

⎝ ⎜ ⎞

⎠ ⎟

31.

�

log x2 + 3x −10( ) ! 32. x = 8! 33. x = 9 (not –3)

34. x =1 (not –1/ 3) ! 35. x = 2! 36. x = 6! 37. x = 5/2 (not –5/ 2)

38. x =15! 39. x =1 (not –4) ! 40. x = 3 (not –1/ 2) ! 41. x = 3!

42.

�

x ∈ 25

, + ∞⎛ ⎝

⎞ ⎠ ! 43.

�

x ∈ −∞ , 13

⎛ ⎝

⎞ ⎠ ! 44.

�

x ∈ −32

, + ∞⎛ ⎝

⎞ ⎠ !

45.

�

x ∈ℜ | x ≠ 0 or

�

x ∈ −∞ , 0( ) ∪ 0 , + ∞( ) ! 46.

�

x ∈ 0 , + ∞( ) ! 47.

�

x ∈ −∞ , 0( ) !

48.

�

f −1 = 2x ! 49.

�

f −1 = ex ! 50.

�

f −1 = 10x−1! 51.

�

f −1 = log3 x

52.

�

f −1 = ln x ! 53.

�

f −1 = log3 x + 2

54. x = 1.40! 55 x = .77! 56. x = 1.13! 57.

�

pH = 6.25!

58.

�

H+[ ] =

�

2.51×10−5 mol / L ! 59. 230 ! 60. 10.2 years!

61. 74.32 grams!62. 5473.93 years! 63. $ 25, 720.41 64. 12.97 years

65)

�

y = 4 x 66)

�

y = 2x+1! 67)

�

y = 3x − 2

Math 370 Chapter 5 Answers! Page 14 of 15! © 2018 Eitel

68)

�

y = (1 4)x + 2 ! 69)

�

y = (1 3)x −1! 70)

�

y = − 1 2( )x

71)

�

y = log2 x ! 72)

�

y = log2 3(x) ! 73)

�

y = log4 (x + 2)

74)

�

y = log1 2(x − 3)! 75)

�

y = log3 4 (−x) ! 76)

�

y = −log5 x

Math 370 Chapter 5 Answers! Page 15 of 15! © 2018 Eitel