473 4.3 Logarithmic Functions CONCEPT PREVIEW Use the properties of logarithms to rewrite each expression. Assume all variables represent positive real numbers. 9. log10 2x 7 10. 3 log4 x - 5 log4 y If the statement is in exponential form, write it in an equivalent logarithmic form. If the statement is in logarithmic form, write it in exponential form. See Example 1. 11. 34 = 81 12. 25 = 32 13. a 2 3b -3 = 27 8 14. 10-4 = 0.0001 15. log6 36 = 2 16. log5 5 = 1 17. log2 3 81 = 8 18. log4 1 64 = -3 Concept Check In Exercises 43–48, match the function with its graph from choices A–F. 43. ƒ1x2 = log2 x 44. ƒ1x2 = log2 2x 45. ƒ1x2 = log2 1 x 46. ƒ1x2 = log2 a 1 2 xb 47. ƒ1x2 = log21x - 12 48. ƒ1x2 = log21-x2 A. 1 1 x y 0 B. 1 1 x y 0 C. 1 1 x y 0 D. 1 1 x y 0 E. 1 1 x y 0 F. 1 0 2 x y Graph each function. See Examples 3 and 4. 49. ƒ1x2 = log5 x 50. ƒ1x2 = log10 x 51. ƒ1x2 = log51x + 12 52. ƒ1x2 = log61x - 22 53. ƒ1x2 = log1/211 - x2 54. ƒ1x2 = log1/313 - x2 55. ƒ1x2 =log31x -1 + 2 56. ƒ1x2 = log21x + 22 - 3 57. ƒ1x2 = log1/21x + 32 - 2 Solve each equation. See Example 2. 19. x = log5 1 625 20. x = log3 1 81 21. logx 1 32 = 5 22. logx 27 64 = 3 23. x = log8 2 4 8 24. x = log 7 2 5 7 25. x = 3log 3 8 26. x = 12log12 5 27. x = 2log2 9 28. x = 8log8 11 29. log x 25 = -2 30. logx 16 = -2 31. log4 x = 3 32. log2 x = 3 33. x = log4 2 3 16 34. x = log 5 2 4 25 35. log9 x = 5 2 36. log4 x = 7 2 37. log1/21x + 32 = -4 38. log1/31x + 62 = -2 39. log1x+32 6 = 1 40. log1x-42 19 = 1 41. 3x - 15 = logx 1 1x 70, x ≠12 42. 4x - 24 = logx 1 1x 70, x ≠12
RkJQdWJsaXNoZXIy NjM5ODQ=