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

• Notes
• 5

This preview shows page 1 - 3 out of 5 pages.

We have textbook solutions for you!
The document you are viewing contains questions related to this textbook. The document you are viewing contains questions related to this textbook.
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
We have textbook solutions for you!
The document you are viewing contains questions related to this textbook. The document you are viewing contains questions related to this textbook.
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 .
• • • 