Homework Help is Here – Start Your Trial Now!
Math
Calculus
a and In 3 = b. Use properties of logarith 31. In 1.5 %3D In

a and In 3 = b. Use properties of logarith 31. In 1.5 %3D In

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
See similar textbooks
icon
Related questions
Topic Video
Question
Please help me with 31,37,43
316 CHAPTER 5 Exponential and Logarithmic Functions Skill Building 16. In ev2 Applic In Prob 87. Ir \ 15. In e 14. log 2-13 20. log69 + log, 4 13. log, 729 \ 19. logs 2 + logs 4 17. 9log, 13 24. log3 8 log, 9 18. eln 8 89. Ir 23. log2 6 log, 8 91. In 21. logs 35 - logs 7 22. logs 16 - logs 2 28. elog 29 93. I 27. eloga 16 25. 4log, 6-log, 26. 5log, 6+log, 7 95. 3 32. In 0,5 97. E 31. In 1.5 29. In 6 30. In 3 99. 36. In 35. In V6 101. 33. In 8 34. In 27 m Problems 37-56, write each expression as a sum and/or difference of logarithms. Express powers as factors. 37. log, 36x 102. 39. logs y 40. log, x 103. 38. log3 9 43. In 44. In (xe*) A 104. 41. In(ex) 42. In - 105. 47. In(x² V1 – x) 0<x<1 45. log, (u?v) u >0, v>0 46. loga a > 0, b > 0 107. V + 1 x > 1 48. In (xV1 + x²) x> 0 50. logs 49. log2 x > 3 x² – 1 109. x - x - 21/3 (x + 4)2 5x² V1 – x - 4(x + 1)2 \51. log x(x + 2) ' Vx + 1 53. In x >0 52. log x > 2 x > 2 (x + 3): (x - 2)2 111. 5x V1 + 3x (x – 4)3 4)272/3 54. In x > 4 x > 4 56. In 0<x<l 55. In x? - 1 113 In Problems 57-70, write each expression as a single logarithm. 57. 3 logs u + 4 logs v 58. 2 log3 u - log3 v 59. log, Vx - log3 r 60. log2 + log2 61. log4 (x – 1) - 5 log4 (x + 1) 62. log (x2 + 3x + 2) – 2 log(x +1 Exp In()- In (x² – 1) 115. x²+2x 64. log 63. Inl ²+ 7x + 6 log x + 2 65. 8 log2 V3x – 2 – log 66. 21 log; V + log3 (9x) – log3 9 67. 2 log,(5x') - log, 116 (2x + 3) 68. log (2 - 70. 3 log5 (3x + 1) - 2 logs(2x – 1) – log5 × In Problems 71-78, use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round vour answer to three decuiur + 1) + 69. 2 log2 (x + 1) – log2(x + 3) – log2(x – 1) 71. log3 21 72. log5 18 73. log1/3 71 75. logv2 7 74. log1/2 15 76. logv5 8 In Problems 79-84, graph each function using a graphing utility and the Change-of-Base Formula. 1 Visde 78. log, V2 77. log, e 79. y = log4 x 80. y = log5 x 82. y = log4 (x – 3) 83. y = log,-1(x + 1) 81. y = log, (x + 2) 85. Mixed Practice If f(x) = In x, g (x) = e", and h (x) = x², find: (a) (fog) (x). What is the domain of fo g? (b) (gof) (x). What is the domain of go f? 84. y = log,+2(x – 2) 86. Mixed Practice If f(x) = log, x, g (x) = -. and h(x) = 4x, find: (c) (fog) (5) (d) (foh) (x). What is the domain of fo h? (e) (foh) (e) (a) (f°g)(x).What is the domain of ƒ ° g! (b) (gºf) (x). What is the domain of g º J ? (c) (fog) (3) (d) (foh)(x). What is the domain of ƒ e H (e) (foh) (8)
Transcribed Image Text:316 CHAPTER 5 Exponential and Logarithmic Functions Skill Building 16. In ev2 Applic In Prob 87. Ir \ 15. In e 14. log 2-13 20. log69 + log, 4 13. log, 729 \ 19. logs 2 + logs 4 17. 9log, 13 24. log3 8 log, 9 18. eln 8 89. Ir 23. log2 6 log, 8 91. In 21. logs 35 - logs 7 22. logs 16 - logs 2 28. elog 29 93. I 27. eloga 16 25. 4log, 6-log, 26. 5log, 6+log, 7 95. 3 32. In 0,5 97. E 31. In 1.5 29. In 6 30. In 3 99. 36. In 35. In V6 101. 33. In 8 34. In 27 m Problems 37-56, write each expression as a sum and/or difference of logarithms. Express powers as factors. 37. log, 36x 102. 39. logs y 40. log, x 103. 38. log3 9 43. In 44. In (xe*) A 104. 41. In(ex) 42. In - 105. 47. In(x² V1 – x) 0<x<1 45. log, (u?v) u >0, v>0 46. loga a > 0, b > 0 107. V + 1 x > 1 48. In (xV1 + x²) x> 0 50. logs 49. log2 x > 3 x² – 1 109. x - x - 21/3 (x + 4)2 5x² V1 – x - 4(x + 1)2 \51. log x(x + 2) ' Vx + 1 53. In x >0 52. log x > 2 x > 2 (x + 3): (x - 2)2 111. 5x V1 + 3x (x – 4)3 4)272/3 54. In x > 4 x > 4 56. In 0<x<l 55. In x? - 1 113 In Problems 57-70, write each expression as a single logarithm. 57. 3 logs u + 4 logs v 58. 2 log3 u - log3 v 59. log, Vx - log3 r 60. log2 + log2 61. log4 (x – 1) - 5 log4 (x + 1) 62. log (x2 + 3x + 2) – 2 log(x +1 Exp In()- In (x² – 1) 115. x²+2x 64. log 63. Inl ²+ 7x + 6 log x + 2 65. 8 log2 V3x – 2 – log 66. 21 log; V + log3 (9x) – log3 9 67. 2 log,(5x') - log, 116 (2x + 3) 68. log (2 - 70. 3 log5 (3x + 1) - 2 logs(2x – 1) – log5 × In Problems 71-78, use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round vour answer to three decuiur + 1) + 69. 2 log2 (x + 1) – log2(x + 3) – log2(x – 1) 71. log3 21 72. log5 18 73. log1/3 71 75. logv2 7 74. log1/2 15 76. logv5 8 In Problems 79-84, graph each function using a graphing utility and the Change-of-Base Formula. 1 Visde 78. log, V2 77. log, e 79. y = log4 x 80. y = log5 x 82. y = log4 (x – 3) 83. y = log,-1(x + 1) 81. y = log, (x + 2) 85. Mixed Practice If f(x) = In x, g (x) = e", and h (x) = x², find: (a) (fog) (x). What is the domain of fo g? (b) (gof) (x). What is the domain of go f? 84. y = log,+2(x – 2) 86. Mixed Practice If f(x) = log, x, g (x) = -. and h(x) = 4x, find: (c) (fog) (5) (d) (foh) (x). What is the domain of fo h? (e) (foh) (e) (a) (f°g)(x).What is the domain of ƒ ° g! (b) (gºf) (x). What is the domain of g º J ? (c) (fog) (3) (d) (foh)(x). What is the domain of ƒ e H (e) (foh) (8)
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Algebraic Operations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS