Please do question 31, 43, 49, 59, and 63.

322 CHAPTER 5 Exponential and Logarithmic Functions 57. 22 + 24 - 12 = EXAMPLE 8 Solving Equations Using a Graphing Utility 61. 16* + 41+1. 65. 3. 4 + 4. 21 Solve: * + et = 2 Express the solution(s) rounded to two decimal places. In Problems 69-82, Solution The solution is found by graphing Y = x + er and 12 is an increasi CALC INTERSECTAUTO REAL RADIAN MP function (do you know why?), there is only one point of intersection for Y, anill 69. log5 ( x + 1 ) Figure 54 shows the graphs of Y, and Y2. Using the INTERSECT command revel \\ 71. et = -x 1 = x + ex that the solution is 0.44, rounded to two decimal places. 75. In x = -x Now Work PROBLEM 71 19. er + In x =4 Y 2 = 2 Intersection Y=2 Mixed Prac Figure 54 In Problems 83 5.6 Assess Your Understanding 83 . 10g2 ( x + [Hint: Ch 'Are You Prepared?' Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red 86. logg x + 1. Solve x2 - 7x - 30 = 0. (pp. A47-A52) 4. Approximate the solution(s) to x - 2x + 2 = 0 using a etex 2. Solve (x + 3) 2 - 4 (x + 3 ) + 3 = 0. (pp. A52-A53) graphing utility. (pp. 26-28) 89. 2 3. Approximate the solution(s) to x3 = x2 - 5 using a graphing [Hint: M utility. (pp. 26-28) 92. 2 Skill Building In Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 5. log4 X = 2 7. log2 ( 5x) = 4 95. f(x ) 6. log (x + 6) = 1 (a) So 8. log3 (3x - 1) = 2 9. log4 (x + 2) = 10g4 8 10. logs (2x + 3) = 10g5 3 ( b ) So (c) So 11. ~ log3 x = 210g3 2 12. -2 log4 x = log4 9 13. 3 log2 x = -log2 27 14. 2 logs x = 3 logs 4 15. 3 log2 (x - 1) + 10g2 4 = 5 16. 2 10g3 (x + 4) - 10g3 9 = 2 (d) S 17. log x + log(x + 15) = 2 (e) S 18. log x + log (x - 21) = 2 19. log (2x + 1) = 1 + log(x - 2) 96. f(x) 20. log (2x) - log (x - 3) = 1 21. log2 ( x + 7 ) + log2 ( x + 8 ) = 1 22. logo (x + 4) + log6(x + 3) = 1 (a) 23. logs(x + 6) = 1 - log8(x + 4) 24. logs (x + 3) = 1 - logs (x - 1) 25. In x + In (x + 2) =4 ( b ) ( C ) 26. In (x + 1) - In x =2 27. log3 (x + 1) + log3 (x + 4) = 2 28. log2 ( x + 1) + log2 (x + 7) = 3 29. 10g1/3 ( x2 + x) - 1081/3(12 - x) = -1 30. log4 (x2 - 9) - 10g4( x + 3) = 3 (d) ( e ) 31. loga (x - 1) - 10ga(x + 6) = 10ga(x - 2) - loga(x + 3) 32. loga x + loga (x - 2) = loga(x + 4) 97. (a) 33. 2 log5 (x - 3) - log58 = 10g52 34. log3 x - 2log3 5 = log3(x + 1) - 210g3 10 35. 2 log6 (x + 2) = 3 10g62 + log64 36. 3 (log7x - log72) = 210874 37. 2 10g13 ( x + 2) = 10813 (4x + 7) 38. log (x - 1) = =log 2 39. (log3 x ) 2 - 5(10g3 X) = 6 40. In x - 3V In x + 2 = 0 In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal 98. places. 41. 2*-5 = 8 42. 5-* = 25 43. 2* = 10 44. 3* = 14 45. 8 * = 1.2 46. 2 * = 1.5 47. 5 (23x ) = 8 48. 0.3 ( 40.2x) = 0.2 49. 31-2x = 4x 50. 2x+1 = 51-2x 51. (=71-x 52. (-5x 53. 1.2* = (0.5 ) -x 54. 0.31+x = 1.72x-1 55. 7 -* = expel puli 56. ex+3 = 17* 93153/10d %001 TIL NOLLDO %001 173HS S MX HECHO EN INDIA VIONI NI 30VW SOSECTION 5.6 Logarithmic and Exponential Equations 323 57. 221 + 2" - 12 = 0 58. 32x + 3* - 2=0 59. 32 + 3*+1 - 4= 0 60. 22x + 2++2 - 12 = 0 61. 16* + 4*+1 - 3 = 0 62. 9t - 3+-1 +1 =0 63. 25* - 8.5* = -16 64. 36* - 6. 61 = - nce Y, is an increasing 65. 3. 4* + 4. 24 + 8 = 0 66. 2 . 49* + 11 . 7* + 5 = 0 67. 4x - 10 .4 * = 3 68. 3* - 14 .3-* =5 rsection for Y, and Yz ECT command reveals peablems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. 69. logs ( x + 1 ) - log4 ( x - 2) = 1 70. logz (x - 1) - log6(x + 2) = 2 \\ 71. et = -x 72. e2x = x + 2 73. et = x2 74. ex = x 75. In = -x 76. In (2x) = -x +2 77. In x = x' - 1 78. In x = -x2 19. er + Inx = 4 80. ex - In x = 4 81. e * = In x 82. ex = - In x Mixed Practice Problems 83-94, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 83. log2 (x + 1) - log4 x = 1 84. log2 (3x + 2) - log4 x = 3 85. log16 x + log4x + log2 x = 7 ages listed in red. [Hint: Change log4 x to base 2.] - 2x + 2 = 0 using a 86. logg x + 3 10g3 x = 14 87. ( V/2) 2- x = 217 88. log2 x1082* = 4 ex te = 1 90 . enter 91. ex - ex 2 2 - = 3 2 Hint: Multiply each side by et.] 92. - ex - e - - 2 2 93. logs x + log3 x = 1 94. log2 x - logo x = 3 [Hint: Use the Change-of-Base Formula.] unded to three decimal 95. f(x) = 10g2 (x + 3) and g (x) = log2 (3x + 1). (b) Shade the region bounded by the y-axis, f(x) = 3*, (a) Solve f(x) = 3. What point is on the graph of f? and g (x) = 10 on the graph drawn in part (a). ogs 3 (b) Solve g (x) = 4. What point is on the graph of g? (c) Solve f(x) = g(x) and label the point of intersection 27 (c) Solve f(x) = g(x). Do the graphs of fand g intersect? on the graph drawn in part (a). If so, where ? 100. (a) Graph f(x) = 2" and g(x) = 12 on the same log3 9 = 2 (d) Solve (f + 8) (x) = 7. Cartesian plane. + log (x - 2) (e) Solve (f - 8) (x) = 2. (b) Shade the region bounded by the y-axis, f(x) = 2t, 96. f(x) = log3 (x + 5) and g (x) = log3(x - 1). and g (x) = 12 on the graph drawn in part (a). 36 ( x + 3 ) = 1 (a) Solve f(x) = 2. What point is on the graph of f? (c) Solve f(x) = g(x) and label the point of intersection = 4 (b) Solve g (x) = 3. What point is on the graph of g? on the graph drawn in part (a). (c) Solve f(x) = g(x) . Do the graphs of f and g intersect? 101. (a) Graph f(x) = 2t+1 and g(x) = 2 *+2 on the same 32 ( x + 7) = 3 If so, where ? Cartesian plane. (d) Solve (f + 8) (x) = 3. (b) Shade the region bounded by the y-axis, f( x) = 2x+1, (e) Solve (f - 8) (x) = 2. and g (x) = 2 *+2 on the graph drawn in part (a). 97. (a) If f(x) = 3*+l and g(x) = 2*+2, graph f and g on the c) Solve f(x) = g(x) and label the point of intersection same Cartesian plane. on the graph drawn in part (a). 83 10 (b) Find the point(s) of intersection of the graphs of f 102. (a) Graph f(x) = 3"x1 and g(x) = 3*-2 on the same and g by solving f(x) = g(x). Round answers to Cartesian plane. three decimal places. Label any intersection points on b) Shade the region bounded by the y-axis, f(x) = 3-x+1 the graph drawn in part (a). (c) Based on the graph, solve f(x) > 8(x). and g (x) = 3* 2 on the graph drawn in part (a). 98. (a) If f(x) = 5*-1 and g(x) = 2*+1, graph f and g on the c) Solve f(x) = g(x) and label the point of intersection on the graph drawn in part (a). ded to three decimal (6 ) same Cartesian plane . (b) Find the point(s) of intersection of the graphs of fand g 103. (a) Graph f(x) = 2x - 4. by solving f(x) = g(x). Label any intersection points (b) Find the zero of f. (c) Based on the graph, solve f( x) 8(x). 104. (a) Graph g (x) = 3* - 9. 2x ) = 0.2 "9. (a) Graph f(x) = 3* and g(x) = 10 on the same (b) Find the zero of g. (c) Based on the graph, solve g(x) > 0. = 51 Cartesian plane