M-370 5 Answers - Los Rios Community College Districtwserver.flc.losrios.edu/~eitel/All PDFS/M-370...
Transcript of M-370 5 Answers - Los Rios Community College Districtwserver.flc.losrios.edu/~eitel/All PDFS/M-370...
Chapter 5 AnswersSection 5 – 0
1.
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x1/2! 2.
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y1 3! 3.
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x1 4 ! 4.
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x2/3! 5.
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x3 4 ! 6.!
�
y4 5
7.
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x7/2! 8.
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x4 2 = x2 ! 9.
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x3 6 = x1/2 ! 10.
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x ! 11.
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y4 ! 12.
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x34
13.
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y35 ! 14.
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x45 ! 15.
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x23 ! 16.
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8x5y7 ! 17.
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−10x6y5! 18.
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−2x7y6
19.
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x2! 20.
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x2 3! 21.
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y7 6! 22.
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x3! 23.
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x 5 4 ! 24.
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x1 4
25.
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x17/12! 26.
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x7 6 ! 27.
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x7 12 ! 28.
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x + x7/6! 29.
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x13/12 + x !
30.
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16x6y8 ! 31.
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8x9y12! 32.
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−27x3y3! 33.
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x4! 34.
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x3! 35.
�
y2
36.
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x1/3 = x3 ! 37.
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x ! 38.
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x1/6! 39.
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y3
x2! 40.
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x4y ! 41.
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y4
x5
42.
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1x3y4
! 43.
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y2
x3! 44.
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x4
9! 45.
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−5y4
2x! 46.
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−12x4y3
! 47.
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−3y8
2x6
48.
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4y7
5x4! 49.
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y ! 50.
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1x2! 51.
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−12x2
! 52.
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1x2! 53.
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x 3
54.
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x9/2! 55.
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x1/12! 56.
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1x1/6
! 57. 4! 58. 9! 59.
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75!
60.
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1112 ! 61. 3! 62. 5! 63.
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23
! 64.
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−54! 65.
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43!
66. 3! 67. 27! 68. 4! 69. 32! 70.
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827! 71.
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49
72.
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64125
! 73.
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169! 74.
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13! 75.
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19
! 76.
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12! 77. 3
78.
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97! 79.
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52! 80.
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43! 81.
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1125
! 82.
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19! 83.
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164!
84.
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14! 85.
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254 ! 86.
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827! 87.
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94
! 88.
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64125
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169
90.
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125216
! 91.
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27125
! 92.
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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