MS-Sol-EE-C04

MS-Sol-EE-C04 - CHAPTER 4 LOGARITHMIC FUNCTIONS Section 4.1...

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CHAPTER 4 LOGARITHMIC FUNCTIONS EXERCISE 4.1 Section 4.1 Properties and graphs of logarithmic functions (page 95) 1. 5 3 = 125 log 5 125 = 3 2. 3 4 = 81 log 3 81 = 4 3. 6 - 2 = 1 36 log 6 1 36 = - 2 4. 10 - 4 = 0.000 1 log 10 0.000 1 = - 4 5. a 7 = 9 log a 9 = 7 6. p r = q log p q = r 7. log 10 100 = 2 10 2 = 100 8. log 5 625 = 4 5 4 = 625 9. 343 1 log 7 = - 3 7 - 3 = 1 343 10. log 1 3 243 = - 5 5 3 1 - = 243 69

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C HAPTER 4 L OGARITHMIC F UNCTIONS 11. log e e 1 = - 1 2 e - 1 2 = 1 e 12. log b c = t b t = c 13. Let y = log 2 32. Then 2 y = 32 2 y = 2 5 y = 5 14. Let y = log 9 3. Then 9 y = 3 3 2 y = 3 2 y = 1 y = 1 2 15. Let y = log 8 0.125. Then 8 y = 0.125 8 y = 1 8 y = - 1 16. Let y = log 1 6 216 . Then y 6 1 = 216 6 - y = 6 3 y = - 3 17. Let y = log a 1. Then a y = 1 y = 0 18. Let y = log a a . Then a y = a y = 1 19. Let y = log b b 3 . Then b y = b 3 y = 3 70
S ECTION 4.1 P ROPERTIES AND G RAPHS OF L OGARITHMIC F UNCTIONS 20. Let y = log e e 1 5 . Then e y = 1 5 e y = - 5 21. Let y = 10 10 7 log . Then log 10 7 = log 10 y y = 7 22. Let y = 5 log a a . Then log a 5 = log a y y = 5 23. log 2 x = 5 x = 2 5 = 32 24. log 5 x = 3 x = 5 3 = 125 25. log 1 3 x = - 4 x = 4 3 1 - = 81 26. log 10 x = - 1 2 x = 2 1 10 - = 1 10 27. log 16 x = 0.25 x = 16 0.25 = 2 28. log x 10 = 1 10 = x 1 x = 10 29. log x 81 = 2 81 = x 2 x = 81 = 9 Note: The base x is positive. 30. log x 4 = 3 2 71

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C HAPTER 4 L OGARITHMIC F UNCTIONS 3 2 x = 4 x = 4 3 2 = 8 31. log x e 1 = - 1 e 1 = x - 1 x = e 32. log x e 3 = - 6 x - 6 = e 3 x = 6 3 - e = 1 e 33. x 0.5 1 2 4 8 16 y = log 4 x - 0.5 0 0.5 1 1.5 2 72
S ECTION 4.1 P ROPERTIES AND G RAPHS OF L OGARITHMIC F UNCTIONS 34. x 0.5 1 5 10 15 20 y = log e x - 0.693 0 1.609 2.303 2.708 2.996 35. x 0.25 0.5 1 2 4 8 y = x 2 1 log 2 1 0 - 1 - 2 - 3 73

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C HAPTER 4 L OGARITHMIC F UNCTIONS 36. x 1 5 1 5 25 125 y = x 5 1 log 1 0 - 1 - 2 - 3 37. x 3 1 1 3 9 y = - log 3 x 1 0 - 1 - 2 38. x 1.5 2 4 6 8 10 y = log e ( x - 1) - 0.693 0 1.099 1.609 1.946 2.197 74
S ECTION 4.1 P ROPERTIES AND G RAPHS OF L OGARITHMIC F UNCTIONS 39. x 3 1 1 3 9 y = 4 - log 3 1 x 3 4 5 6 40. x - 2.5 - 2 - 1 0 2 5 y = log e ( x + 3) - 2 - 2.693 - 2 - 1.307 - 0.901 - 0.391 0.079 41. Note: The graph of y = x a log - is the mirror image of the graph of y = x a log about the x - axis. 75

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HAPTER 4 L OGARITHMIC F UNCTIONS 42. Note: The graph of y = ) ( log x a - is the mirror image of the graph of y = x a log about the y - axis. 43. Note: The graph of y = ) ( log a x a - can be obtained by shifting the graph of y = x a log a units to the right. 44. Note: The graph of y = x a log - a can be obtained by shifting the graph of y = x a log a units downward. 76
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MS-Sol-EE-C04 - CHAPTER 4 LOGARITHMIC FUNCTIONS Section 4.1...

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