# Properties of Logarithms and Solving Exponential Equations

# Properties of Logarithms and Solving Exponential Equations

In Exercises 1-10, use a calculator to

evaluate the function at the given value

p. Round your answer to the nearest

hundredth.

1. f(x) = log _{4}(x); p = 57.60.

2. f(x) = log _{4}(x); p = 11.22.

3. f(x) = log _{7}(x); p = 2.98.

4. f(x) = log_{3}(x); p = 2.27.

5. f(x) = log_{6}(x); p = 2.56.

6. f(x) = log_{8}(x); p = 289.27.

7. f(x) = log_{8}(x); p = 302.67.

8. f(x) = log_{5}(x); p = 15.70.

9. f(x) = log_{8}(x); p = 46.13.

10. f(x) = log_{4}(x); p = 15.59.

In Exercises 11-18, perform each of the

following tasks.

a) Approximate the solution of the given

equation using your graphing calculator .

Load each side of the equation

into the Y= menu of your calculator .

Adjust the WINDOW parameters

so that the point of intersection of

the graphs is visible in the viewing

window. Use the intersect utility

in the CALC menu of your calculator

to determine the x- coordinate of the

point of intersection. Then make an

accurate copy of the image in your

viewing window on your homework

paper.

b) Solve the given equation algebraically ,

and round your answer to the nearest

hundredth.

11. 20 = 3(1.2)^{x}

12. 15 = 2(1.8)^{x}

13. 14 = 1.4^{5x}

14. 16 = 1.8^{4x}

15. −4 = 0.2^{x} − 9

16. 12 = 2.9^{x} + 2

17. 13 = 0.1^{x+1}

18. 19 = 1.2^{x-6}

In Exercises 19-34, solve the given equation

algebraically , and round your answer

to the nearest hundredth.

19. 20 = e^{x-3}

20. −4 = e^{x} − 9

21. 23 = 0.9^{x} + 9

22. 10 = e^{x} + 7

23. 19 = e^{x} + 5

24. 4 = 7(2.3)^{x}

25. 18 = e^{x+4}

26. 15 = e^{x+6}

27. 8 = 2.7^{3x}

28. 7 = e^{x+1}

29. 7 = 1.1^{8x}

30. 6 = 0.2^{x-8}

31. −7 = 1.3^{x} − 9

32. 11 = 3(0.7)^{x}

33. 23 = e^{x} + 9

34. 20 = 3.2^{x+1}

35. Suppose that you invest $17,000 at

6% interest compounded daily . How many

years will it take for your investment to

double? Round your answer to the nearest

hundredth.

36. Suppose that you invest $6,000 at

9% interest compounded continuously . How

many years will it take for your investment

to double? Round your answer to

the nearest hundredth.

37. Suppose that you invest $16,000 at

6% interest compounded daily. How many

years will it take for your investment to

reach $26,000? Round your answer to

the nearest hundredth.

38. Suppose that you invest $15,000 at

5% interest compounded monthly. How

many years will it take for your investment

to double? Round your answer to

the nearest hundredth.

39. Suppose that you invest $18,000 at

3% interest compounded monthly. How

many years will it take for your investment

to double? Round your answer to

the nearest hundredth.

40. Suppose that you invest $7,000 at

5% interest compounded daily. How many

years will it take for your investment to

reach $13,000? Round your answer to

the nearest hundredth.

41. Suppose that you invest $16,000 at

9% interest compounded continuously. How

many years will it take for your investment

to double? Round your answer to

the nearest hundredth.

42. Suppose that you invest $16,000 at

2% interest compounded continuously. How

many years will it take for your investment

to reach $25,000? Round your answer

to the nearest hundredth.

43. Suppose that you invest $2,000 at

5% interest compounded continuously. How

many years will it take for your investment

to reach $10,000? Round your answer

to the nearest hundredth.

44. Suppose that you invest $4,000 at

6% interest compounded continuously. How

many years will it take for your investment

to reach $10,000? Round your answer

to the nearest hundredth.

45. Suppose that you invest $4,000 at

3% interest compounded daily. How many

years will it take for your investment to

reach $14,000? Round your answer to

the nearest hundredth.

46. Suppose that you invest $13,000 at

2% interest compounded monthly. How

many years will it take for your investment

to reach $20,000? Round your answer

to the nearest hundredth.

47. Suppose that you invest $20,000 at

7% interest compounded continuously. How

many years will it take for your investment

to reach $30,000? Round your answer

to the nearest hundredth.

48. Suppose that you invest $16,000 at

4% interest compounded continuously. How

many years will it take for your investment

to double? Round your answer to

the nearest hundredth.

49. Suppose that you invest $8,000 at

8% interest compounded continuously. How

many years will it take for your investment

to double? Round your answer to

the nearest hundredth.

50. Suppose that you invest $3,000 at

3% interest compounded daily. How many

years will it take for your investment to

double? Round your answer to the nearest

hundredth.

**8.6 Answers**

1. 2.92

3. 0.56

5. 0.52

7. 2.75

9. 1.84

11.

a)

b) 10.41

13.

a)

b) 1.57

15.

a)

b) −1.00

17.

a)

b) −2.11

19. 6.00

21. −25.05

23. 2.64

25. −1.11

27. 0.70

29. 2.55

31. 2.64

33. 2.64

35. 11.55 years

37. 8.09 years

39. 23.13 years

41. 7.70 years

43. 32.19 years

45. 41.76 years

47. 5.79 years

49. 8.66 years

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