only 34,36,56,58,60,62,64,66

please and thank you

218 Chapter 3 Exponential Solving an Exponential Equation In Exercises 55-80, Finding the Zero of a Function In Exercise: 87-90, use solve the exponential equation algebraically. Round your graphing utility to graph the function and approximate result to three decimal places. Use a graphing utility to its zero accurate to three decimal places. verify your answer. 87. g(x) = 6el-x - 25 88. f(x) = 303x/2 - 962 55. 83x = 360 56. 65x = 3000 89. g(1) = 20.09 - 3 90. h(t) = 0.125 - 8 57. 5-1/2 = 0.20 58. 4-31 = 0.10 59. 250e0.02r = 10,000 60. 100e0.005x = 125,000 Solving a Logarithmic Equation In Exercises 91-112. solve the logarithmic equation algebraically. Round the 61. 500ex = 300 62. 1000e-4x = 75 result to three decimal places. Verify your answer using 63. 7 - 2ex = 5 64. - 14 + 3ex = 11 a graphing utility. 65. 5(23 -x) -13=100 66. 6(8-2-*) +15 = 2601 91. In x = -3 92. In x = -4 67. 1 + 0.10 12 = 2 68. (16 + 0.878 31 = 30 93. In 4x = 2.1 94. In 2x = 1.5 12 26 95. logs(3x + 2) = logs(6 - x) 69. 5000 (1 + 0.005) = 250,000 96. log, (4 + x) = log,(2x - 1) 0.005 97. - 2 + 2 In 3x = 17 98. 3 + 2 In x = 10 70. 250 (1 + 0.01)*1 = 150,000 0.01 99. 7 log, (0.6x) = 12 100. 4 10g10(X - 6) = 11 / 71. e2x - 4ex - 5= 0 72. e2x - 5ex + 6 = 0 101. log10(2 - 3) = 2 102. 10g10 72 = 6 73. ex = ex 2 - 2 74. e2x = ex2 -8 103. In Vx + 2 = 1 104. In Vx - 8 = 5 75. ex - 3x = ex-2 76. ex = ex2-2x 105. In(x + 1)2 = 2 106. In(x2 + 1) = 8 400 525 107. log4 x - logA(x - 1) = 2 77. - Itex = 350 78. = 275 108. log3 x + log3(x - 8) = 2 79. 40 50 109. In(x + 5) = In(x - 1) - In(x + 1) 1 - 5e-0.01x = 200 80. 1 - 2e-0.001x = 1000 110. In(x + 1) - In(x - 2) = In x 111. 10g10 8x - 10g10( 1 + Vx) = 2 Algebraic-Graphical-Numerical In Exercises 81 and 82, (a) complete the table to find an interval containing the 112. 10g10 4x - 10g10( 12 + Vx) = 2 solution of the equation, (b) use a graphing utility to graph both sides of the equation to estimate the solution, The Change-of-Base Formula In Exercises 113 and 114 and (c) solve the equation algebraically. Round your use the method of Example 10 to prove the change-of-bas results to three decimal places. formula for the indicated base. 81. e3x = 12 /113. 10ga X = 10ge x log a 114. 10ga x = log 10-X 0.6 log 10 a 0.7 0.8 0.9 1.0 Algebraic-Graphical-Numerical In Exercises 115-11 (a) complete the table to find an interval containing th 82. 20(100 - ex/2) = 500 solution of the equation, (b) use a graphing utility graph both sides of the equation to estimate the solution 5 6 7 8 9 and (c) solve the equation algebraically. Round you results to three decimal places. 20(100 - ex/2) 115. In 2x = 2.4 Solving an Exponential Equation Graphically In 2 3 4 5 6 Exercises 83-86, use the zero or root feature or the zoom In 2x and trace features of a graphing utility to approximate the solution of the exponential equation accurate to three decimal places. 116. 3 In 5x = 10 83. 1 0.065 3651 365 = 4 84. 4 - 2.471 9: X 4 5 6 7 40 = 21 8 85. 3000 = 2 86. 119 3 In 5x 2+ e2x ex - 14 =7a graphing utility. see Appendix A. Vocabulary and Concept Check In Exercise 1 and 2, fill in the blank. 1. To solve exponential and logarithmic equations, you can use the following One-to-One and Inverse Properties. (a) at = a" if and only if (b) loga x = loga y if and only if ( c ) aloga* = (d) loga at = 2. An solution does not satisfy the original equation. 3. What is the value of In e?? 4. Can you solve 5* = 125 using a One-to-One Property? 5. What is the first step in solving the equation 3 + In x = 10? 6. Do you solve logA x = 2 by using a One-to-One Property or an Inverse Property? Procedures and Problem Solving Checking Solutions In Exercises 7-14, determine 21. f(x) = In ex+1 22. f (x) = In ex- 2 whether each x-value is a solution of the equation. 8 (x) = 2x + 5 8 (x) = 3x + 2 7. 42x - 7 = 64 8. 23x+1 = 32 (a) x = 5 Solving an Exponential Equation In Exercises 23-36, (a) x = -1 ( b ) x = 2 solve the exponential equation. ( b ) x = 2 9. 3ex+ 2 = 75 23. 4* = 16 24. 3x = 243 10. 4ex-1 = 60 (a) x = -2+ e25 25. 5x = 375 26. 7* = 49 (a) x = 1 + In 15 (b ) x = -2+ In 25 - 27. (8) = 64 28. ()* = 32 ( b ) x ~ 3.7081 (c) x = 1.2189 29. G)* = 16 30. ( 4)* = 27 11. log,(3x) = 3 (c) x = In 16 31. ex = 14 32. et = 66 12. logo (3x) = 2 (a) x - 21.3560 33. 6(10r) = 216 34. 5(8*) = 325 (b ) x =-4 (a) x ~ 20.2882 35. 2x+3 = 256 36. 3x - 1 = 31 (c) x = 64 (b) x = 108 5 Solving a Logarithmic Equation In Exercises 37-46, 13. In(x - 1) = 3.8 (c) x = 7.2 14. In(2 + x) = 2.5 solve the logarithmic equation. (a) x = 1 + e3.8 38. In x - In 2 = 0 (b) x = 45.7012 (a) x = e2.5 - 2 37. In x - In 5 = 0 40. In x = - 14 ( b ) x = 4073 ( c ) x = 1 + In 3.8 400 39. In x = -9 42. log, 25 = 2 (c ) x = 2 41. log, 625 = 4 44. 10g10* = -2 Solving Equations Graphically In Exercises 15-22, use a 43. 10g10* = - 1 graphing utility to graph f and g in the same viewing 46. In(3x + 5) = 8 45. In(2x - 1) = 5 algebraically. window. Approximate the point of intersection of the graphs of f and g. Then solve the equation f(x) = g(x) Using Inverse Properties In Exercises 47-54, simplify 15. f (x ) = 2x the expression. 48. In e 2x - 1 8 (x ) = 8 47. In etz 16. f(x) = 27* 50. eln(x2+ 2) 17. f(xx ) = 5x-2- 15 49. eln.x2 g(x ) = 10 g (x ) = 9 51. - 1 + In e2x 19. f(x) = 4 log3X 18. f (x) = 2-*+1 -3 52. -4 + eln.x4 8(x) = 20 8 (x) = 13 53. 5 + eln(12+ 1) 20. f(x) = 3 10g5 x 54. 3 - In(ex2+ 2) g (x) = 6