Section 8.6
Properties of Logarithms; Solving Exponential Equations
841
8.6 Exercises
In Exercises 1-10, use a calculator to
evaluate the function at the given value
p. Round your answer to the nearest
hundredth.
paper.
b) Solve the given equation algebraically,
and round your answer to the nearest
hundredth.
1.
f (x) = log4 (x); p = 57.60.
11.
20 = 3(1.2)x
2.
f (x) = log4 (x); p = 11.22.
12.
15 = 2(1.8)x
3.
f (x) = log7 (x); p = 2.98.
13.
14 = 1.45x
4.
f (x) = log3 (x); p = 2.27.
14.
16 = 1.84x
5.
f (x) = log6 (x); p = 2.56.
15.
−4 = 0.2x − 9
6.
f (x) = log8 (x); p = 289.27.
16.
12 = 2.9x + 2
7.
f (x) = log8 (x); p = 302.67.
17.
13 = 0.1x+1
8.
f (x) = log5 (x); p = 15.70.
18.
19 = 1.2x−6
9.
f (x) = log8 (x); p = 46.13.
In Exercises 19-34, solve the given equation algebraically, and round your answer to the nearest hundredth.
10.
f (x) = log4 (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
1
19.
20 = ex−3
20.
−4 = ex − 9
21.
23 = 0.9x + 9
22.
10 = ex + 7
23.
19 = ex + 5
24.
4 = 7(2.3)x
25.
18 = ex+4
26.
15 = ex+6
27.
8 = 2.73x
Copyrighted material. See: http://msenux.redwoods.edu/IntAlgText/
Version: Fall 2007
842
Chapter 8
28.
7 = ex+1
29.
7 = 1.18x
30.
6 = 0.2x−8
31.
−7 = 1.3x − 9
32.
11 = 3(0.7)x
33.
23 = ex + 9
34.
20 = 3.2x+1
Exponential and Logarithmic Functions
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.
Version: Fall 2007
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.
Section 8.6
Properties of Logarithms; Solving Exponential Equations
843
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.
Version: Fall 2007
844
Chapter 8
Exponential and Logarithmic Functions
8.6 Answers
1.
2.92
15.
3.
0.56
a)
5.
0.52
7.
2.75
9.
1.84
11.
b) −1.00
a)
17.
a)
b) 10.41
13.
b) −2.11
a)
b) 1.57
Version: Fall 2007
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
Section 8.6
Properties of Logarithms; Solving Exponential Equations
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
845
Version: Fall 2007