# MATH 101 instructions (48) - SECTION 5.5 Properties of...

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Chapter 1 / Exercise 77
Applied Calculus
Berresford/Rockett
Expert Verified
SECTION 5.5 Properties of Logarithms 303 5.5 Assess Your Understanding 1. 2. 3. 4. 5. 6. 7. log a M r = log a a M N b = - log a ( MN ) = + log a a r = a log a M = log a a = log a 1 = 8. . 9. If then . 10. True or False 11. True or False 12. True or False ln 8 ln 4 = 2 log 2 1 3 x 4 2 = 4 log 2 1 3 x 2 ln 1 x + 3 2 - ln 1 2 x 2 = ln 1 x + 3 2 ln 1 2 x 2 M = log 8 M = log 5 7 log 5 8 , If log a x = log a 6, then x = Concepts and Vocabulary Skill Building In Problems 13–28, use properties of logarithms to find the exact value of each expression. Do not use a calculator. 13. log 3 3 71 14. log 2 2 - 13 15. ln e - 4 16. ln e 2 2 17. 2 log 2 7 18. e ln 8 19. log 8 2 + log 8 4 20. log 6 9 + log 6 4 21. log 6 18 - log 6 3 22. log 8 16 - log 8 2 23. log 2 6 # log 6 8 24. log 3 8 # log 8 9 25. 3 log 3 5 - log 3 4 26. 5 log 5 6 + log 5 7 27. e log e 2 16 28. e log e 2 9 29. ln 6 30. ln 2 3 31. ln 1.5 32. ln 0.5 33. ln 8 34. ln 27 35. ln 2 5 6 36. ln A 4 2 3 37. log 5 1 25 x 2 38. log 3 x 9 39. log 2 z 3 40. log 7 x 5 41. ln 1 ex 2 42. ln e x 43. ln x e x 44. ln 1 xe x 2 In Problems 29–36, suppose that and Use properties of logarithms to write each logarithm in terms of a and b. ln 3 = b . ln 2 = a In Problems 37–56, write each expression as a sum and/or difference of logarithms. Express powers as factors . 45. log a 1 u 2 v 3 2 u 7 0, v 7 0 46. log 2 a a b 2 b a 7 0, b 7 0 47. ln A x 2 2 1 - x B 0 6 x 6 1 48. ln A x 4 1 + x 2 B x 7 0 49. log 2 ¢ x 3 x - 3 x 7 3 50. log 5 ¢ 4 3 x 2 + 1 x 2 - 1 x 7 1 51. log B x 1 x + 2 2 1 x + 3 2 2 R x 7 0 52. log B x 3 2 x + 1 1 x - 2 2 2 R x 7 2 53. ln B x 2 - x - 2 1 x + 4 2 2 R 1 > 3 x 7 2 54. ln B 1 x - 4 2 2 x 2 - 1 R 2 > 3 x 7 4 55. ln 5 x 2 1 + 3 x 1 x - 4 2 3 x 7 4 56. ln B 5 x 2 2 3 1 - x 4 1 x + 1 2 2 R 0 6 x 6 1 63. ln a x x - 1 b + ln a x + 1 x b - ln 1 x 2 - 1 2 64. log ¢ x 2 + 2 x - 3 x 2 - 4 - log ¢ x 2 + 7 x + 6 x + 2 65. 8 log 2 2 3 x - 2 - log 2 a 4 x b + log 2 4 57. 3 log 5 u + 4 log 5 v 58. 2 log 3 u - log 3 v 59. log 3 1 x - log 3 x 3 60. log 2 a 1 x b + log 2 ¢ 1 x 2 61. log 4 1 x 2 - 1 2 - 5 log 4 1 x + 1 2 62. log 1 x 2 + 3 x + 2 2 - 2 log 1 x + 1 2 In Problems 57–70, write each expression as a single logarithm . PDFill PDF Editor with Free Writer and Tools
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Chapter 1 / Exercise 77
Applied Calculus
Berresford/Rockett
Expert Verified
304 CHAPTER 5 Exponential and Logarithmic Functions In Problems 71–78, use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places . 66. 21 log 3 1 3 x + log 3 1 9 x 2 2 - log 3 9 67. 2 log a 1 5 x 3 2 - 1 2 log a 1 2 x + 3 2 68. 1 3 log 1 x 3 + 1 2 + 1 2 log 1 x 2 + 1 2 69. 2 log 2 1 x + 1 2 - log 2 1 x + 3 2 - log 2 1 x - 1 2 70. 3 log 5 1 3 x + 1 2 - 2 log 5 1 2 x - 1 2 - log 5 x 71. log 3 21 72. log 5 18 73. log 1 > 3 71 74. log 1 > 2 15 75. log 2 2 7 76. log 2 5 8 77. log p e 78. log p 2 2 In Problems 79–84, graph each function using a graphing utility and the Change-of-Base Formula .