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CTION 5.6 Logarithmic and Exponential Equations 323 In Problems 45-72, solve each exponential equation. Express irrational solutions in exact form. 45. 2-3 = 8 46. 5= 25 47. 2= 10 49. 8 = 1.2 50. 2 = 1.5 48. 3' = 14 51. 5(2) = 8 52. 0.3 (402) = 0.2 53. 31-2 = 4" 54. 2*+1 = 51-20 1-x 55. = 71- 56. = 5* (0.5) 61. 22 + 2" - 12 = 0 - 3 = 0 58. 0.31+* = 1.72r-1 62. 32 + 3* - 2 = 0 66. 9* - 3*+1 + 1 = 0 57. 1.2" = %3D 59. 7- = e* 60. et+3 63. 32 + 3r+1- 4 = 0 65. 16 + 4*+ 69. 3-4* + 4.2" + 8 = 0 64. 22 + 2*+2- 12 = 0 67. 25 - 8 5 = -16 71. 4 - 10.4 = 3 68. 36" - 6.6 = -9 72. 3 - 14.3 = 5 70. 2-49 + 11-7 + 5 = 0 %3D

CTION 5.6 Logarithmic and Exponential Equations 323 In Problems 45-72, solve each exponential equation. Express irrational solutions in exact form. 45. 2-3 = 8 46. 5= 25 47. 2= 10 49. 8 = 1.2 50. 2 = 1.5 48. 3' = 14 51. 5(2) = 8 52. 0.3 (402) = 0.2 53. 31-2 = 4" 54. 2*+1 = 51-20 1-x 55. = 71- 56. = 5* (0.5) 61. 22 + 2" - 12 = 0 - 3 = 0 58. 0.31+* = 1.72r-1 62. 32 + 3* - 2 = 0 66. 9* - 3*+1 + 1 = 0 57. 1.2" = %3D 59. 7- = e* 60. et+3 63. 32 + 3r+1- 4 = 0 65. 16 + 4*+ 69. 3-4* + 4.2" + 8 = 0 64. 22 + 2*+2- 12 = 0 67. 25 - 8 5 = -16 71. 4 - 10.4 = 3 68. 36" - 6.6 = -9 72. 3 - 14.3 = 5 70. 2-49 + 11-7 + 5 = 0 %3D

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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SECTION 5.6 Logarithmic and Exponential Equations 323 sing fun Dableus 45-72, solve each exponential equation. Express irrational solutions in exact form. 46. 5* = 25 45. 2-5 = 8 47. 2 = 10 48. 3 = 14 50. 2* = 1.5 49. 8 = 1,2 51. 5(2) = 8 52. 0.3 (40.2x) = 0.2 54. 2*+1 = 5!-2r 1-x 53. 31-2r = 4" = 71- 55. 56. = 5* 57. 1.2 = (0.5)-* 61. 22 + 2" - 12 = 0 65. 16" + 4**1 - 3 = 0 69. 3-4* + 4.2" + 8 = 0 58. 0.31+* = 1.72r-1 59. 7-X = er 60. er+3 = T 62. 32r + 3* - 2 = 0 63. 32r + 3r+1 - 4 = 0 64. 22 + 2r+2 – 12 = 0 66. 9* - 3*+1 + 1 = 0 70. 2.49 + 11.7 + 5 = 0 67. 25* - 8. 5* = - 16 68. 36* - 6.6* = -9 71. 4 - 10-4 = 3 72. 3 - 14.3- = 5 a le Problems 73–86, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. 73. logs (x + 1) – log4(x - 2) = 1 74. log2 (x - 1) - log.(x + 2) = 2 77. e = x 76. e2* = x + 2 75. e = -x 78. e = x 79. In x = -x 80. In (2x) = -x + 2 81. In x = x³ - 1 82. In x = -x2 83. e* + In x = 4 84. e - In x = 4 85. e* = In x 86. e* -In x Applications and Extensions 87. f(x) = log2 (*+ 3) and g(x) = log2(3x + 1). (a) Solve f(x) = 3. What point is on the graph of f? (b) Solve g(x) = 4. What point is on the graph of g? (c) Solve f(x) = g(x). Do the graphs of fand g intersect? If so, where? (d) Solve (f + g) (x) = 7. (e) Solve (f - 8) (x) = 2. 88. f(x) = log3 (x + 5) and g (x) = log3 (x (a) Solve f(x) = 2. What point is on the graph of f? (b) Solve g(x) = 3. What point is on the graph of g? (c) Solve f(x) = g(x). Do the graphs of f and g intersect? If so, where? (d) Solve (f + g) (x) = 3. (e) Solve (f - g) (x) = 2. 89. (a) If f(x) = 3*+1 and g (x) = 2**2, graphf and g on the same Cartesian plane. (b) Find the point(s) of intersection of the graphs of f and g by solving f(x) = g(x). Round answers to three decimal places. Label any intersectita point an the graph drawn in part (a). (c) Based on the graph, solve f(x) > 8x). 90. (a) If f(x) = 5*-1 and g(x) = 2*+1, graph f and g on ihe same Cartesian plane. (b) Find the point(s) of intersection of the graphs of f and g by solving f(x) = g(x). Label any intersection points on the graph drawn in part (a). (c) Based on the graph, solve f(x) > g(x). 91. (a) Graph f(x) = 3* and g (x) = 10 on the same Cartesian plane. (b) Shade the region bounded by the y-axis, f(x) = 3*, and g (x) = 10 on the graph drawn in part (a). (c) Solve f(x) = g(x) and label the point of intersection on the graph drawn in part (a). 2. (a) Graph f(x) = 2* and g (x) = 12 on the same Cartesian plane. 93. (a) Graph f(x) = 2*+1 and g(x) = 2*+2 on the same Cartesian plane. (b) Shade the region bounded by the y-axis, f(x) = 2*+1 and g(x) = 2*+2 on the graph drawn in part (a). (c) Solve f(x) = g(x) and label the point of intersection on the graph drawn in part (a). ed in nl 94. (a) Graph f(x) = 3-x+1 and g(x) = 3*-2 on the same Cartesian plane. (b) Shade the region bounded by the y-axis, f(x) = 3*+1, and g (x) = 3*2 on the graph drawn in part (a). (c) Solve f(x) = g(x) and label the point of intersection on the graph drawn in part (a). 1). 1-AS 2=D 95. (a) Graph f(x) = 2* – 4. (b) Find the zero of f. (c) Based on the graph, solve f(x) < 0. 96. (a) Graph g (x) = 3* - 9. (b) Find the zero of g. (c) Based on the graph, solve g (x) > 0. 97. A Population Model The resident population of the United States in 2018 was 327 million people and was growing at a rate of 0.7% per year. Assuming that this growth rate continues, the model P(t) = 327 (1.007)-2018 represent the population P (in millions of people) in year t. (a) According to this model, when will the population of th United States be 415 million people? (b) According to this model, when will the population of th United States be 470 million people? Source: U.S. Census Bureau 98. A Population Model The population of the world in 20 was 7.63 billion people and was growing at a ra of 1.1% per year. Assuming that this growth rate continu the model P(t) = 7.63 (1.011)-2018 population P (in billions of people) in year t. (a) According to this model, when will the population of world be 9 billion people? (b) According to this model, when will the population of world be 12.5 billion people? represents t (b) Shade the region bounded by the y-axis, f(x) = 2*, and g (x) = 12 on the graph drawn in part (a). (c) Solve f(x) = g(x) and label the point of intersection on the graph drawn in part (a). Source: U.S. Census Bureau and
Transcribed Image Text:SECTION 5.6 Logarithmic and Exponential Equations 323 sing fun Dableus 45-72, solve each exponential equation. Express irrational solutions in exact form. 46. 5* = 25 45. 2-5 = 8 47. 2 = 10 48. 3 = 14 50. 2* = 1.5 49. 8 = 1,2 51. 5(2) = 8 52. 0.3 (40.2x) = 0.2 54. 2*+1 = 5!-2r 1-x 53. 31-2r = 4" = 71- 55. 56. = 5* 57. 1.2 = (0.5)-* 61. 22 + 2" - 12 = 0 65. 16" + 4**1 - 3 = 0 69. 3-4* + 4.2" + 8 = 0 58. 0.31+* = 1.72r-1 59. 7-X = er 60. er+3 = T 62. 32r + 3* - 2 = 0 63. 32r + 3r+1 - 4 = 0 64. 22 + 2r+2 – 12 = 0 66. 9* - 3*+1 + 1 = 0 70. 2.49 + 11.7 + 5 = 0 67. 25* - 8. 5* = - 16 68. 36* - 6.6* = -9 71. 4 - 10-4 = 3 72. 3 - 14.3- = 5 a le Problems 73–86, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. 73. logs (x + 1) – log4(x - 2) = 1 74. log2 (x - 1) - log.(x + 2) = 2 77. e = x 76. e2* = x + 2 75. e = -x 78. e = x 79. In x = -x 80. In (2x) = -x + 2 81. In x = x³ - 1 82. In x = -x2 83. e* + In x = 4 84. e - In x = 4 85. e* = In x 86. e* -In x Applications and Extensions 87. f(x) = log2 (*+ 3) and g(x) = log2(3x + 1). (a) Solve f(x) = 3. What point is on the graph of f? (b) Solve g(x) = 4. What point is on the graph of g? (c) Solve f(x) = g(x). Do the graphs of fand g intersect? If so, where? (d) Solve (f + g) (x) = 7. (e) Solve (f - 8) (x) = 2. 88. f(x) = log3 (x + 5) and g (x) = log3 (x (a) Solve f(x) = 2. What point is on the graph of f? (b) Solve g(x) = 3. What point is on the graph of g? (c) Solve f(x) = g(x). Do the graphs of f and g intersect? If so, where? (d) Solve (f + g) (x) = 3. (e) Solve (f - g) (x) = 2. 89. (a) If f(x) = 3*+1 and g (x) = 2**2, graphf and g on the same Cartesian plane. (b) Find the point(s) of intersection of the graphs of f and g by solving f(x) = g(x). Round answers to three decimal places. Label any intersectita point an the graph drawn in part (a). (c) Based on the graph, solve f(x) > 8x). 90. (a) If f(x) = 5*-1 and g(x) = 2*+1, graph f and g on ihe same Cartesian plane. (b) Find the point(s) of intersection of the graphs of f and g by solving f(x) = g(x). Label any intersection points on the graph drawn in part (a). (c) Based on the graph, solve f(x) > g(x). 91. (a) Graph f(x) = 3* and g (x) = 10 on the same Cartesian plane. (b) Shade the region bounded by the y-axis, f(x) = 3*, and g (x) = 10 on the graph drawn in part (a). (c) Solve f(x) = g(x) and label the point of intersection on the graph drawn in part (a). 2. (a) Graph f(x) = 2* and g (x) = 12 on the same Cartesian plane. 93. (a) Graph f(x) = 2*+1 and g(x) = 2*+2 on the same Cartesian plane. (b) Shade the region bounded by the y-axis, f(x) = 2*+1 and g(x) = 2*+2 on the graph drawn in part (a). (c) Solve f(x) = g(x) and label the point of intersection on the graph drawn in part (a). ed in nl 94. (a) Graph f(x) = 3-x+1 and g(x) = 3*-2 on the same Cartesian plane. (b) Shade the region bounded by the y-axis, f(x) = 3*+1, and g (x) = 3*2 on the graph drawn in part (a). (c) Solve f(x) = g(x) and label the point of intersection on the graph drawn in part (a). 1). 1-AS 2=D 95. (a) Graph f(x) = 2* – 4. (b) Find the zero of f. (c) Based on the graph, solve f(x) < 0. 96. (a) Graph g (x) = 3* - 9. (b) Find the zero of g. (c) Based on the graph, solve g (x) > 0. 97. A Population Model The resident population of the United States in 2018 was 327 million people and was growing at a rate of 0.7% per year. Assuming that this growth rate continues, the model P(t) = 327 (1.007)-2018 represent the population P (in millions of people) in year t. (a) According to this model, when will the population of th United States be 415 million people? (b) According to this model, when will the population of th United States be 470 million people? Source: U.S. Census Bureau 98. A Population Model The population of the world in 20 was 7.63 billion people and was growing at a ra of 1.1% per year. Assuming that this growth rate continu the model P(t) = 7.63 (1.011)-2018 population P (in billions of people) in year t. (a) According to this model, when will the population of world be 9 billion people? (b) According to this model, when will the population of world be 12.5 billion people? represents t (b) Shade the region bounded by the y-axis, f(x) = 2*, and g (x) = 12 on the graph drawn in part (a). (c) Solve f(x) = g(x) and label the point of intersection on the graph drawn in part (a). Source: U.S. Census Bureau and
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