x 5 x 5 2 x 2 5 1 2 x 32 12 x 3 x 3 4 x 4 3 1 4 x 64 13 x 2 ln x ln 2 ln x ln 2

X 5 x 5 2 x 2 5 1 2 x 32 12 x 3 x 3 4 x 4 3 1 4 x 64

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x 5 x 5 2 x 2 5 1 2 x 32 12. x 3 x 3 4 x 4 3 1 4 x 64 13. x 2 ln x ln 2 ln x ln 2 0 14. x 5 ln x ln 5 ln x ln 5 0 15. x 0.693 x ln 2 ln e x ln 2 e x 2 16. x 1.386 x ln 4 ln e x ln 4 e x 4 17. x 0.368 x e 1 e ln x e 1 ln x 1 18. x 0.000912 x e 7 e ln x e 7 ln x 7 19. x 64 x 4 3 4 log 4 x 4 3 log 4 x 3 20. or 0.008 x 1 125 x 5 3 log 5 x 3 21. Point of intersection: 3, 8 x 3 2 x 2 3 2 x 8 f x g x 22. Point of intersection: 2 3 , 9 x 2 3 27 x 27 2 3 27 x 9 f x g x 23. Point of intersection: 9, 2 x 9 x 3 2 log 3 x 2 f x g x 24. Point of intersection: 5, 0 x 5 x 4 1 e ln x 4 e 0 ln x 4 0 f x g x 25. x 1 or x 2 0 x 1 x 2 0 x 2 x 2 x x 2 2 e x e x 2 2 26. x 2, x 4 x 4 x 2 0 x 2 2 x 8 0 2 x x 2 8 e 2 x e x 2 8 27. By the Quadratic Formula or x 0.618. x 1.618 x 2 x 1 0 x 2 3 x 2 e x 2 3 e x 2
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488 Chapter 5 Exponential and Logarithmic Functions 28. x 0, x 1 2 x x 1 0 2 x 2 2 x 0 x 2 x 2 2 x e x 2 e x 2 2 x 29. x 1.465 x log 3 5 log 5 log 3 or ln 5 ln 3 log 3 3 x log 3 5 3 x 5 4 3 x 20 30. x 1.723 x ln 16 ln 5 x log 5 16 5 x 16 2 5 x 32 31. x ln 5 1.609 ln e x ln 5 e x 5 2 e x 10 32. x ln 91 4 3.125 ln e x ln 91 4 e x 91 4 4 e x 91 33. x ln 28 3.332 ln e x ln 28 e x 28 e x 9 19 34. x 2.015 x ln 37 ln 6 x log 6 37 6 x 37 6 x 10 47 35. x ln 80 2 ln 3 1.994 2 x ln 3 ln 80 ln 3 2 x ln 80 3 2 x 80 36. x ln 3000 5 ln 6 0.894 5 x ln 3000 ln 6 5 x ln 6 ln 3000 ln 6 5 x ln 3000 6 5 x 3000 37. t 2 t 2 1 5 t 2 5 1 5 t 2 1 5 5 t 2 0.20 38. t ln 0.10 3 ln 4 0.554 3 t ln 0.10 ln 4 3 t ln 4 ln 0.10 ln 4 3t ln 0.10 4 3 t 0.10 39. x 4 x 1 3 3 x 1 3 3 3 x 1 27 40. x 8 x 3 5 x 3 log 2 32 2 x 3 32 41. 3 ln 565 ln 2 6.142 x 3 ln 2 ln 565 ln 2 x ln 2 3 ln 2 ln 565 x ln 2 ln 565 3 ln 2 3 ln 2 x ln 2 ln 565 3 x ln 2 ln 565 ln 2 3 x ln 565 2 3 x 565 42. x ln 431 ln 64 ln 8 4.917 x ln 8 ln 431 ln 64 x ln 8 ln 431 ln 8 2 2 ln 8 x ln 8 ln 431 2 x ln 8 ln 431 ln 8 2 x ln 431 8 2 x 431
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Section 5.4 Exponential and Logarithmic Equations 489 43. 0.059 x 1 3 log 3 2 3 x log 3 2 log 10 3 x log 3 2 10 3 x 12 8 8 10 3 x 12 44. 6.146 x 6 log 7 5 x 6 log 7 5 log 10 x 6 log 7 5 10 x 6 7 5 5 10 x 6 7 45. x 1 ln 7 ln 5 2.209 x 1 ln 7 ln 5 x 1 ln 5 ln 7 ln 5 x 1 ln 7 5 x 1 7 3 5 x 1 21 46. x 6 ln 5 ln 3 4.535 x ln 5 ln 3 6 6 x ln 5 ln 3 6 x ln 3 ln 5 ln 3 6 x ln 5 3 6 x 5 8 3 6 x 40 47. x ln 12 3 0.828 3 x ln 12 e 3 x 12 48. x ln 50 2 1.956 2 x ln 50 ln e 2 x ln 50 e 2 x 50 49. x ln 3 5 ln 5 3 0.511 x ln 3 5 e x 3 5 500 e x 300 50. x 1 4 ln 3 40 0.648 4 x ln 3 40 ln e 4 x ln 3 40 e 4 x 3 40 1000 e 4 x 75 51. x ln 1 0 e x 1 2 e x 2 7 2 e x 5 52. x ln 25 3 2.120 ln e x ln 25 3 e x 25 3 3 e x 25 14 3 e x 11 53. x 1 3 log 8 3 log 2 1 0.805 3 x 1 log 2 8 3 log 8 3 log 2 or ln 8 3 ln 2 log 2 2 3 x 1 log 2 8 3 2 3 x 1 8 3 6 2 3 x 1 16 6 2 3 x 1 7 9
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490 Chapter 5 Exponential and Logarithmic Functions 54. x 3 ln 3.5 2 ln 4 2.548 2 x 6 ln 3.5 ln 4 6 2 x ln 3.5 ln 4 6 2 x log 4 3.5 4 6 2 x 3.5 8 4 6 2 x 28 8 4 6 2 x 13 41 55. or (No solution) x ln 5 1.609 e x 5 e x 1 e x 1 e x 5 0 e 2 x 4 e x 5 0 56. x ln 2 0.693 or x ln 3 1.099 e x 2 or e x 3 e x 2 e x 3 0 e 2 x 5 e x 6 0 57. Not possible since for all x . e x 4 0 e x 4 x ln 4 1.386 e x > 0 e x 1 0 e x 1 e x 1 e x 4 0 e 2 x 3 e x 4 0 58.
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  • Natural logarithm, Logarithm, Inverse Property

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