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LOGARITHM TEST REVIEW Graph each of the following. 1. y log 4 x 2. f ( x) log 1 x 3 Find the inverse of each of the following. F1 I y GJ H9 K x 3. y = 7 x 4. f ( x ) log 9 x 5. 6. f ( x ) log w x 7. y = zx Write the exponential equation in logarithmic form. 8. 34 = 81 9. 4 1 12. 16 2 1 4 3 3 1 16 10. 9 2 27 11. ab =12 1 13. 72 7 14. mn = p Write the logarithmic equation in exponential form. 15. log 3 9 2 16. log 5 25 1 2 1 2 b2 20. log11 11 Solve each equation. 22. log 3 x 2 23. log x 16 4 19. logb 26. log 64 30. 1 y 8 27. log x 2 log 1 (4 x 7) 2 17. log x y 4 1 2 1 4 18. log8 4 2 3 21. log a b c 24. log 4 x 2 28. log 1 8 y 25. log 8 32 x 29. log16 ( 3x 1) 2 31. log 3 (2 y 3) log 3 ( y 6) 3 32. log5 ( x 2 2) log5 (10x 18) 33. log2 ( x 2 14 x) 5 Use the laws of logarithms to expand each expression. 34. log 3 mn 35. log 4 a 3b 36. log 1 ( ab) 3 37. log 7 xy 2 m n 38. log 3 3 x5 39. log 2 3 y 3 Fx I 40. log GJ Hy K 42. log a b c 43. log 2a b Use the laws of logarithms to rewrite as a single logarithm. 4 6 41. log 5 4 x 1 2 44. log p log q 45. 4 logb 48. 3(log a log b) 49. 46. 2 log a 3 log b 1 log a 6 log b 3 47. log a 3 log b 50. log a 4 log b 2 log c Solve each equation. 51. log 4 8 log 4 3 log 4 6 x 54. log 7 x 3 log 7 2 57. log 7 x 53. log x log 52. 2 log 5 log n 55. 4 log5 x log5 4 log5 4 1 1 log 7 144 log 7 8 2 3 56. log 4 ( x 3) log 4 ( x 3) 2 58. log5 ( x 3) log5 x log5 4 Evaluate each of the following to the nearest ten-thousandth. 59. log 2 15 60. log 7 21 61. log 3 5 Solve for x to the nearest hundredth. 62. 3x 39 63. 287 4 x 64. 7 x 3 20 65. 32 x1 54 66. 53x 263 67. 43 x2 801 68. 4 x 187 . 69. 52 x 34 x 1 70. 4 x 63x 7 ANSWER KEY 1 log 20 4 y = 4x 1. x -3 -2 -1 0 1 2 3 y 1/64 1/16 ¼ 1 4 16 64 3. y-1 = log7x 8. 4 = log3 81 12. 1 1 = log16 4 2 15. 3 2 = 9 19. b-2 = 1 b2 y = log4x y = (1/3)x y = log1/3x x y 1/64 -3 1/16 -2 ¼ -1 1 0 4 1 16 2 64 3 2. x -3 -2 -1 0 1 2 3 x 27 9 3 1 1/3 1/9 1/27 4. f-1(x) = 9x 5. y-1 = log1/9x 9. -3 = log4 13. 1 16 1 = log7 7 2 1 2 16. 5 25 20. 112 11 10. y 27 9 3 1 1/3 1/9 1/27 6. f-1(x) = wx 3 = log9 27 2 7. y-1 = logzx 11. b = loga 12 14. n = logm p 4 17. x = y 1 21. ac = b 18. y -3 -2 -1 0 1 2 3 2 3 8 4 22. x = 9 23. x = 2 24. x = 1 16 25. x = 5 3 26. y = 1 2 27. x = 4 28. y = -3 29. x = 1 30. x = 1 2 31. y = 9 32. x =8 or x = 2 33. x = -2 or x = 16 34. log 3 m log 3 n 35. 3 log 4 a log 4 b 36. 3 log 1 a 3 log 1 b 2 37. 1 log 7 x log 7 y 2 40. 4 log 6 x 4 log 6 y 38. 1 log 3 m log 3 n 2 39. 5 log 2 x 3 log 2 y 41. 1 log 5 x 4 42. 3 log a log b 45. logb 4 46. 48. Fa I a logGJor log Hb K b 43. log 2 3 log a log b 44. log pq a 47. log 3 b 3 log a 2b 3 3 3 3 49. log a b6 ab 4 50. log 2 c 51. x = 4 52. n = 25 53. x = 5 54. x = 8 55. x = 2 56. x = 5 57. x = 6 58. x = 1 59. 3.9069 60. 1.5646 61. 1.4650 62. x = 3.33 63. x = 4.08 64. x = 1.46 65. x = 1.32 66. x = 1.15 67. x = 2.27 68. x = .45 69. x = .93 70. x = -3.14 2 1 log c 2