55,67 SECTION 5.6 Logarithmic and Exponential Equations 323sing funDableus 45-72, solve each exponential equation. Express irrational solutions in exact form.46. 5* = 2545. 2-5 = 847. 2 = 1048. 3 = 1450. 2* = 1.549. 8 = 1,251. 5(2) = 852. 0.3 (40.2x) = 0.254. 2*+1 = 5!-2r1-x53. 31-2r = 4"= 71-55.56.= 5*57. 1.2 = (0.5)-*61. 22 + 2" - 12 = 065. 16" + 4**1 - 3 = 069. 3-4* + 4.2" + 8 = 058. 0.31+* = 1.72r-159. 7-X = er60. er+3 = T62. 32r + 3* - 2 = 063. 32r + 3r+1 - 4 = 064. 22 + 2r+2 – 12 = 066. 9* - 3*+1 + 1 = 070. 2.49 + 11.7 + 5 = 067. 25* - 8. 5* = - 1668. 36* - 6.6* = -971. 4 - 10-4 = 372. 3 - 14.3- = 5a 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) = 174. log2 (x - 1) - log.(x + 2) = 277. e = x76. e2* = x + 275. e = -x78. e = x79. In x = -x80. In (2x) = -x + 281. In x = x³ - 182. In x = -x283. e* + In x = 484. e - In x = 485. e* = In x86. e*-In xApplications and Extensions87. 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 thesame Cartesian plane.(b) Find the point(s) of intersection of the graphs of f and gby solving f(x) = g(x). Round answers to threedecimal places. Label any intersectita point an thegraph 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 ihesame Cartesian plane.(b) Find the point(s) of intersection of the graphs of f and gby solving f(x) = g(x). Label any intersection pointson 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 Cartesianplane.(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 intersectionon the graph drawn in part (a).2. (a) Graph f(x) = 2* and g (x) = 12 on the same Cartesianplane.93. (a) Graph f(x) = 2*+1 and g(x) = 2*+2 on the sameCartesian plane.(b) Shade the region bounded by the y-axis, f(x) = 2*+1and g(x) = 2*+2 on the graph drawn in part (a).(c) Solve f(x) = g(x) and label the point of intersectionon the graph drawn in part (a).ed in nl94. (a) Graph f(x) = 3-x+1 and g(x) = 3*-2 on the sameCartesian 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 intersectionon the graph drawn in part (a).1).1-AS2=D95. (a) Graph f(x) = 2* – 4.(b) Find the zero of f.(c) Based on the graph, solve f(x) 0.97. A Population Model The resident population of the UnitedStates in 2018 was 327 million people and was growing ata rate of 0.7% per year. Assuming that this growth ratecontinues, the model P(t) = 327 (1.007)-2018 representthe population P (in millions of people) in year t.(a) According to this model, when will the population of thUnited States be 415 million people?(b) According to this model, when will the population of thUnited States be 470 million people?Source: U.S. Census Bureau98. A Population Model The population of the world in 20was 7.63 billion people and was growing at a raof 1.1% per year. Assuming that this growth rate continuthe model P(t) = 7.63 (1.011)-2018population P (in billions of people) in year t.(a) According to this model, when will the population ofworld be 9 billion people?(b) According to this model, when will the population ofworld 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 intersectionon the graph drawn in part (a).Source: U.S. Census Bureauand

Question

55,67 SECTION 5.6 Logarithmic and Exponential Equations 323sing funDableus 45-72, solve each exponential equation. Express irrational solutions in exact form.46. 5* = 2545. 2-5 = 847. 2 = 1048. 3 = 1450. 2* = 1.549. 8 = 1,251. 5(2) = 852. 0.3 (40.2x) = 0.254. 2*+1 = 5!-2r1-x53. 31-2r = 4&#34;= 71-55.56.= 5*57. 1.2 = (0.5)-*61. 22 + 2&#34; - 12 = 065. 16&#34; + 4**1 - 3 = 069. 3-4* + 4.2&#34; + 8 = 058. 0.31+* = 1.72r-159. 7-X = er60. er+3 = T62. 32r + 3* - 2 = 063. 32r + 3r+1 - 4 = 064. 22 + 2r+2 – 12 = 066. 9* - 3*+1 + 1 = 070. 2.49 + 11.7 + 5 = 067. 25* - 8. 5* = - 1668. 36* - 6.6* = -971. 4 - 10-4 = 372. 3 - 14.3- = 5a 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) = 174. log2 (x - 1) - log.(x + 2) = 277. e = x76. e2* = x + 275. e = -x78. e = x79. In x = -x80. In (2x) = -x + 281. In x = x³ - 182. In x = -x283. e* + In x = 484. e - In x = 485. e* = In x86. e*-In xApplications and Extensions87. 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 thesame Cartesian plane.(b) Find the point(s) of intersection of the graphs of f and gby solving f(x) = g(x). Round answers to threedecimal places. Label any intersectita point an thegraph 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 ihesame Cartesian plane.(b) Find the point(s) of intersection of the graphs of f and gby solving f(x) = g(x). Label any intersection pointson 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 Cartesianplane.(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 intersectionon the graph drawn in part (a).2. (a) Graph f(x) = 2* and g (x) = 12 on the same Cartesianplane.93. (a) Graph f(x) = 2*+1 and g(x) = 2*+2 on the sameCartesian plane.(b) Shade the region bounded by the y-axis, f(x) = 2*+1and g(x) = 2*+2 on the graph drawn in part (a).(c) Solve f(x) = g(x) and label the point of intersectionon the graph drawn in part (a).ed in nl94. (a) Graph f(x) = 3-x+1 and g(x) = 3*-2 on the sameCartesian 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 intersectionon the graph drawn in part (a).1).1-AS2=D95. (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 UnitedStates in 2018 was 327 million people and was growing ata rate of 0.7% per year. Assuming that this growth ratecontinues, the model P(t) = 327 (1.007)-2018 representthe population P (in millions of people) in year t.(a) According to this model, when will the population of thUnited States be 415 million people?(b) According to this model, when will the population of thUnited States be 470 million people?Source: U.S. Census Bureau98. A Population Model The population of the world in 20was 7.63 billion people and was growing at a raof 1.1% per year. Assuming that this growth rate continuthe model P(t) = 7.63 (1.011)-2018population P (in billions of people) in year t.(a) According to this model, when will the population ofworld be 9 billion people?(b) According to this model, when will the population ofworld 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 intersectionon the graph drawn in part (a).Source: U.S. Census Bureauand

Accepted Answer

Solution of the problem as follows