Answer log-functions-b
- 1. The Logarithmic Functions Answers. 1. log5(25) = 2 3. log2(32) = 5 7. log4(1/4) = –1 a+b7. logv(ab) = –2 9. logk( ) = 2 11. ln(1/e2) = –2a–b 13. ln(4) = –3v 15. log (A – B) = r – t 17. 33 = 27 19. 5–2 = 1/25 21. b–2 = 9 23. a – b = u2 25. 100 = 102 27. y = 10–2x 29. ert = A/P 31. ≈ 0.699 33. ≈ 1.699 35. ≈ 2.699 37. ±3.699 39. ≈ –2.20 41. ≈ –3.20 43. ≈ –4.20 45. x = 16 47. ≈ 1/16 49. x = 23 51. x = –13 53. x = 2/3 55. x = 6 57. x = 2 59. x = 1/2 61. x = –13 63. x = 2/3 65. x = 6 67. x = 2 69. x = 1/2 Properties of Logarithm Answers. 1. 2log(x) – 3log(y) 3. 2log(x) – (3/2)log(y) 5. 5log (x) + 2log(y) 7. (5/2)log (x) + (2/3)log(y) + (2/3)log(z)
- 2. Properties of Logarithm 9. log (1 – x) + 2log(x) 11. log(1 + x2) + 2log(x) 13. 1 + log(x) 15. ½ + log (x – 3) 17. –3ln(x) – 4 19. log (3x2) 21. log (3/x) 23. log( )3–x 3+x 25. log( )x √3+x 27. 2 29. –x 31. rt 33. 3x – 5y 35. 3x – 5y 37. 7 39. x 41. 400 43. 9√e Equations That Do Not Need Calculators Answers. 1. x = 1 3. x = 2/5 5. x = 1/3 7. x = 1 9. x = 5/13 11. x = –7 13. x = 1/7 15. x = –1/7 17. x = –1/2 19. x = 8 21. x = 1 23. x = 3 25. x = –½ 27. x = 5 29. x = 2 31.no solution 33. x = 5/3 35. x = –½ 37. x = 5 39. x =1 41. x = 3 43. no solution 45. no solution
- 3. Answers. 1. t = ln(12/5) /0.03 ≈ 29.2 yr 3. t = ln(12/5) /0.09 ≈ 9.73 yr 5. r = ln(12/5) / 4 ≈ 21.2 % 7. r = ln(12/5) / 12 ≈ 8.75 % Applications of Log and Exp 9. ln(2/5)/(–0.03) ≈ 30.5 yr 11. ln(2/5)/(–0.09) ≈ 10.2 yr 13. r = ln(2/5) / 4 ≈ –23.0 % 15. r = ln(2/5) / 12 ≈ –7.64 % 17. ln(10)/0.075 ≈ 30.7 yr 19. ln(3)/0.036 ≈ 30.5 yr 21. ln(5)/20 ≈ 8.05% 23. ln(5)/5 ≈ 32.2% 25. ln(3/4)/5 ≈ -2.88% 27. 36, 24, 18, 12, 9, 8, 6, 4, and 3 years respectively 29. 54, 36, 27, 18, 12, 9, 6, and 4 years respectively