Problem 11,13,15,16,17,18 no sketches
Exercises 4.3 Just in Time Exercises the 1. V 13 In Exercises 1-4, write each number using a rational exponent. 2. V4 3. Ve In Exercises 5-8, f and g are inverses of each other. 4. Ves 5. True or False: If f(2) = 3, then f-1(3) = 2. Assume fis one-to-one. 3. True or False: If g (8) = 2, then g(2) = 8. Assume g is one-to-one. 7. True or False: If f(x) = 4, then its inverse exists, and is f-1(x) = 3. True or False: If f and g are inverses, then g(x) = J(x) In Exercises 9 and 10, write each number using scientific notation. 9. 0.036 10. 102,000,000 Skills In Exercises 11 and 12, complete the table by filling in the exponential statements that are equivalent to the given logarithmic statements. 11 . Exponential 12. Statement Statement ogarithmic Exponential log , 1 = 0 Statement Statement log 10 = 1 log,4 = 2 log 100 = 2 log = = - 1 log, = -2 log x = b, a > 0, a # 1 log a = b , a >0 In Exercises 13 and 14, complete the table by filling in the logarithmic statements that are equivalent to the given exponential statements. 13. 14 Exponential Loganthmic Exponential Logarithmic Statement Statement Statement Statement 34 = 81 35 = 243 5 1/3 = V5 712 = V7 6-1 =1 6-2 - 1 36 10 = 6 a" = 1, a > 0, a # 1 355 Chapter 4 Exponential and Logarithmic Functions 356 In Exercises 15-34, evaluate each expression without using a calculator. Round answers to four decimal place 17. log V 10 18. log V 10 15. log 10000 16. log 0.001 20. In Ve 21. In el/3 22. In- 19. In ez 26. In e" 23. log 10*+y 24. In ex - z 25. log 10* 1 27. log, V2 28. log, 49 29. 109 3 21 30. log , 7 32. log 9 33. log, 4* +1 34. log, 6ax 31. 10g, /2 4 In Exercises 35-42, evaluate the expression to four decimal places using a calculator. Round answers to for decimal places. 35. 2log4 36. -310g6 37. In V2 38. In 39. log 1400 40. log 2500 41. 2 In _ 42. -In - In Exercises 43-50, use the change-of-base formula to evaluate the following using a calculator. Round answers to four decimal places. 43. log, 1.25 44. log, 2.75 15. log, 0.5 16. log, 0.65 47. log, 12 48. log, 20 49. log , 150 50. log, 230 In Exercises 51-56, use the definition of a logarithm to solve for x. 51. log, x = 3 52. log, V5 = x 53. log, x = 54. log x = -2 55. log 216 = 3 56. log 9 = In Exercises 57-72, find the domain of each function. Use your answer to help graph the function, and label all asymptotes and intercepts. 57. f(x) = 2logx 58. f(x) = 41nx 59. f(x) = 410g, x 60. f(x) = 310g, x 61. g(x) = (log x) - 3 62. h(x) = (In x) + 2 63. f(x) = log,(x + 1) 64. f(x) = 10g (x - 2) 65. f(x) = In(x + 4) 66. f(x) = log(x - 3) 67. g(x) = 2log, (x - 1) 68. f(x) = -log,(x+3) 69. f(t) = 10g13 70. 8(s) = 1081 12 S 71. f(x) = loglal 72. g (x) = In (x7) 73. Use the following graph of f(x) = 10* to estimate log 7. Explain how you obtained your answer. f(x) = 10* 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 *
