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Mathematics LibreTexts

4.3E: Logarithmic Functions (Exercises)

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section 4.3 exercise

Rewrite each equation in exponential form

1. log4(q)=m

2. log3(t)=k

3. loga(b)=c

4. logp(z)=u

5.log(v)=t

6. log(r)=s

7. ln(w)=n

8. ln(x)=y

Rewrite each equation in logarithmic form.

9. 4x=y

10. 5y=x

11. cd=k

12. nz=L

13. 10a=b

14. 10p=v

15. ek=h

16. ey=x

Solve for x.

17. log3(x)=2

18. log4(x)=3

19. log2(x)=3

20. log5(x)=1

21. log(x)=3

22. log(x)=5

23. ln(x)=2

24. ln(x)=2

Simplify each expression using logarithm properties.

25. log5(25)

26. log2(8)

27. log3(127)

28. log6(136)

29. log6(6)

30. log5(35)

31. log(10,000)

32. log(100)

33. log(0.001)

34. log(0.00001)

35. ln(e2)

36. ln(e3)

Evaluate using your calculator.

37. log(0.04)

38. log(1045)

39. ln(15)

40. ln(0.02)

Solve each equation for the variable.

41. 5x=14

42. 3x=23

43. 7x=115

44. 3x=14

45. e5x=17

46. e3x=12

47. 34x5=38

48. 42x3=44

49. 1000(1.03)t=5000

50. 200(1.06)t=550

51. 3(1.04)3t=8

52. 2(1.08)4t=7

53. 50e0.12t=10

54. 10e0.03t=4

55. 108(12)x=5

56. 100100(14)x=70

Convert the equation into continuous growth form, f(t)=aekt.

57. f(t)=300(0.91)t

58. f(t)=120(0.07)t

59. f(t)=10(1.04)t

60. f(t)=1400(1.12)t

Convert the equation into annual growth form, f(t)=abt.

61. f(t)=150e0.06t

62. f(t)=100e0.12t

63. f(t)=50e0.012t

64. f(t)=80e0.85t

65. The population of Kenya was 39.8 million in 2009 and has been growing by about 2.6% each year. If this trend continues, when will the population exceed 45 million?

66. The population of Algeria was 34.9 million in 2009 and has been growing by about 1.5% each year. If this trend continues, when will the population exceed 45 million?

67. The population of Seattle grew from 563,374 in 2000 to 608,660 in 2010. If the population continues to grow exponentially at the same rate, when will the population exceed 1 million people?

68. The median household income (adjusted for inflation) in Seattle grew from $42,948 in 1990 to $45,736 in 2000. If it continues to grow exponentially at the same rate, when will median income exceed $50,000?

69. A scientist begins with 100 mg of a radioactive substance. After 4 hours, it has decayed to 80 mg. How long after the process began will it take to decay to 15 mg?

70. A scientist begins with 100 mg of a radioactive substance. After 6 days, it has decayed to 60 mg. How long after the process began will it take to decay to 10 mg?

71. If $1000 is invested in an account earning 3% compounded monthly, how long will it take the account to grow in value to $1500?

72. If $1000 is invested in an account earning 2% compounded quarterly, how long will it take the account to grow in value to $1300?

Answer

1. 4m=q

3. ac=b

5. 10t=v

7. en=w

9. log4(y)=x

11. logc(k)=d

13. log(b)=a

15. ln(h)=k

17. 9

19. 1/8

21. 1000

23. e2

25. 2

27. -3

29. 1/2

31. 4

33. -3

35. -2

37. -1.398

39. 2.708

41. log(14)log(5)1.6397

43. log(115)log(7)1.392

45. ln(17)51.6397

47. log(38)log(3)+542.078

49. log(5)log(1.03)54.449

51. log(83)3log(1.04)8.335

53. ln(15)0.121.6397

55. log(58)log(12)1.6397

57. f(t)=300e0.0943t

59. f(t)=10e0.03922t

61. f(t)=150(1.0618)t

63. f(t)=50(0.98807)t

65. During the year 2013

67. During the year 2074

69. 34 hours

71. 13.532 years


This page titled 4.3E: Logarithmic Functions (Exercises) is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by David Lippman & Melonie Rasmussen (The OpenTextBookStore) via source content that was edited to the style and standards of the LibreTexts platform.

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