Name: ________________________ Class: ___________________ Date: __________
PreCalc 12 Chapter 5 Part 3 Rev Pack v1
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Which logarithm is equal to log 2 (x  9 )  log 2 (x  5 ) ?
Ê
ˆ
A. log 4 ÁÁ x 2  14x  45 ˜˜
Ë
¯
B. log 2 (2x  14)
____
2. Solve: log18  log3  logx
A. x  15
B. x  54
____
5
192
2
B. x 
3
log 6
log 5
log4500
B. x 
log 30
log750
log5
D. x  log 250
C. x 
Ö 143.25
D. x 
Ö 0.22
C. x 
Ö 2.91
D. x 
Ö 4.91
7. An account pays 3.6% annual interest, compounded monthly.
What is the interest rate per compounding period, as a decimal?
A. 3.6
B. 0.003
____
C. x 
6. Solve: 220  3 x  2
Give the solution to the nearest hundredth.
A. x 
Ö 71.33
B. x 
Ö 4.9
____
D. x  5
5. Solve: 573  4 x
Give the solution to the nearest hundredth.
A. x 
Ö 4.58
B. x 
Ö 2.76
____
C. x  14
Ê
ˆ
4. What is the solution of the equation 6 ÁÁ 5 x  3 ˜˜  4500?
Ë
¯
A. x 
____
C. x  6
D. x  21
3. Solve: 256 x  1  64 x  6
A. x 
____
Ê
ˆ
C. log 2 ÁÁ x 2  14x  45 ˜˜
Ë
¯
D. log 2 (x  14 )
C. 0.3
D. 0.036
8. To repay a loan, Chloe makes payments bi-monthly (every 2 months) for 4 years.
How many payments does she make?
A. 24
B. 4
C. 10
D. 6
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ID: A
Name: ________________________
____
ID: A
12t
9. Use the equation 400  200 (1.003) to determine the time in years (to the nearest year) it will take an
investment of $200 to double when it is invested in an account that pays 3.6% annual interest, compounded
monthly.
A. 10 years
B. 1 year
C. 19 years
D. 20 years
____ 10. The Richter scale measures the intensity of an earthquake. The magnitude, M, of an earthquake can be
ÊÁ I ˆ˜
determined using the function M  log ÁÁÁÁ ˜˜˜˜ , where I microns is the intensity of the earthquake, and S microns
ËS ¯
is the intensity of a standard earthquake.
In June 2011, New Zealand experienced an earthquake with magnitude 6.0.
Calculate the intensity of the earthquake in New Zealand in terms of a standard earthquake.
A. 10 60 S
B. 10 6 S
C. 6S
D. 60S
____ 11. The decibel scale measures the intensity of sound. The loudness of a sound, L decibels (dB), can be
ÊÁ I ˆ˜
determined using the function L  10log ÁÁÁÁ ˜˜˜˜ , where I is the intensity of the sound and I 0 is the intensity of
ÁË I 0 ˜¯
the quietest sound that can be detected.
The loudness of a night club is 110 dB.
Calculate the intensity of this sound in terms of I 0 .
A. 11I 0
C. 10 110 I 0
B. 10 11 I 0
D. 110I 0
____ 12. The Richter scale measures the intensity of an earthquake. The magnitude, M, of an earthquake can be
ÁÊ I ˜ˆ
determined using the function M  log ÁÁÁÁ ˜˜˜˜ , where I microns is the intensity of the earthquake, and S microns
ËS ¯
is the intensity of a standard earthquake.
In November 2011, Oklahoma experienced an earthquake with magnitude 4.7.
In September 2011, Argentina experienced an earthquake with magnitude 6.7.
How many times as intense as the Oklahoma earthquake was the Argentina earthquake?
A. 10 3 times as intense
B. 10 2 times as intense
C. 3 times as intense
D. Approximately 1.4 times as intense
____ 13. The decibel scale measures the intensity of sound. The loudness of a sound, L decibels (dB), can be
ÊÁ I ˆ˜
determined using the function L  10log ÁÁÁÁ ˜˜˜˜ , where I is the intensity of the sound and I 0 is the intensity of
ÁË I 0 ˜¯
the quietest sound that can be detected.
The loudness of a vacuum cleaner is 80 dB and the loudness of a snowmobile is 120 dB.
How many times as intense as the sound of a vacuum cleaner is the sound of a snowmobile?
A. 10 4 times as intense
B. 10 40 times as intense
C. 40 times as intense
D. 1.5 times as intense
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Name: ________________________
ID: A
____ 14. The pH scale measures the acidity or alkalinity of a solution. A solution that has a pH of 7 is neutral. For each
increase of 1 pH, a solution is 10 times as alkaline. For each decrease of 1 pH, a solution is 10 times as acidic.
A sample of soap has a pH of 9.5. A sample of household ammonia has a pH of 11.3.
To the nearest whole number, how many times as alkaline as the soap is the ammonia?
A. 12 times as alkaline
B. 2 times as alkaline
C. 33 times as alkaline
D. 63 times as alkaline
____ 15. The pH scale measures the acidity or alkalinity of a solution. A solution that has a pH of 7 is neutral. For each
increase of 1 pH, a solution is 10 times as alkaline. For each decrease of 1 pH, a solution is 10 times as acidic.
A sample of juice has a pH of 2.9. A sample of milk has a pH of 6.6.
To the nearest whole number, how many times as acidic as the milk is the juice?
A. 23 times as acidic
B. 2 times as acidic
C. 1339 times as acidic
D. 5012 times as acidic
____ 16. The future value formula is used when an amount, FV dollars, is saved through a series of equal investments
at equal time intervals, and the compounding period of the interest is equal to the time interval for the
R[(1  i) n  1]
investments. The formula is: FV 
, where R dollars is the regular investment, i is the interest
i
rate per compounding period, and n is the number of investments.
A student wants to buy a French horn in 13 months for $1700. The student plans to make 13 equal monthly
deposits into a savings account that pays 4% annual interest, compounded monthly.
How much should the student deposit each month?
A. $2.11
B. $128.17
C. $102.24
D. $13.79
____ 17. The future value formula is used when an amount, FV dollars, is saved through a series of equal investments
at equal time intervals, and the compounding period of the interest is equal to the time interval for the
R[(1  i) n  1]
investments. The formula is: FV 
, where R dollars is the regular investment, i is the interest
i
rate per compounding period, and n is the number of investments.
To the nearest month, how many monthly investments of $200 would have to be made into a savings account
that pays 5% annual interest, compounded monthly, for the future value to be $13 601.22?
A. 10
B. 30
C. 60
D. 975
____ 18. The present value formula is used when an amount, PV dollars, is borrowed and then repaid through a series
of equal payments at equal time intervals, and the compounding period of the interest is equal to the time
interval for the payments. The first payment is made after a time equal to the compounding period. The
R[1  (1  i) n ]
, where R dollars is the regular payment, i is the interest rate per
formula is: PV 
i
compounding period, and n is the number of payments.
A person has a balance of $508.62 on a credit card. The credit card charges 19% annual interest, compounded
monthly. The minimum payment is $15 per month. If the person does not make any more purchases using the
card, and pays only the minimum payment each month, how long will it take before the balance is paid off, to
the nearest month?
A. 49 months
B. 27 months
C. 20 months
D. 55 months
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Name: ________________________
ID: A
Short Answer
19. Determine whether x  4 is a root of this equation.
log (x  9 )  log (x  6 )  1
Ê
ˆ
20. Solve: 65  5 ÁÁ 4 x  3 ˜˜
Ë
¯
Give the exact solution using logs.
21. Solve: 3 x  9  5 x  6
Give the exact solution using logs.
22. Solve: log 6 50  log 6 (x  2 )  log 6 (x  7 )
23. Solve: log 2 (x  16 )  log 2 (x  7 )  1  log 2 (x  2 )  log 2 (x  3 )
24. The pH scale measures the acidity or alkalinity of a solution. A solution that has a pH of 7 is neutral. For each
increase of 1 pH, a solution is 10 times as alkaline. For each decrease of 1 pH, a solution is 10 times as acidic.
The pH of each of two unknown substances is measured. Substance A has a pH of 2.5 and Substance B has a
pH of 2.1. Which substance is more acidic?
25. The future value formula is used when an amount, FV dollars, is saved through a series of equal investments
at equal time intervals, and the compounding period of the interest is equal to the time interval for the
R[(1  i) n  1]
, where R dollars is the regular investment, i is the interest
investments. The formula is: FV 
i
rate per compounding period, and n is the number of investments.
Each month, Raj deposits $30 into a savings account with an annual interest rate of 1.9%, compounded
monthly. How much will Raj have in the account after 4 years?
26. The present value formula is used when an amount, PV dollars, is borrowed and then repaid through a series
of equal payments at equal time intervals, and the compounding period of the interest is equal to the time
interval for the payments. The first payment is made after a time equal to the compounding period. The
R[1  (1  i) n ]
, where R dollars is the regular payment, i is the interest rate per
formula is: PV 
i
compounding period, and n is the number of payments.
A student borrows $5500 to buy a used car. The loan has an annual interest rate of 8.1%, compounded
monthly. The loan will be repaid after 3 years. How much are the monthly payments?
27. The compound interest formula is used when an amount, A dollars, is saved after making a single investment
of A 0 dollars in an account that earns i percent annual interest, with n compounding periods per year, for t
nt
ÊÁ
i ˆ˜˜˜
Á
Á
years. The formula is: A  A 0 ÁÁ 1  ˜˜
n¯
Ë
To the nearest year, how long will it take an investment of $700 to triple at an annual interest rate of 4.5%,
compounded quarterly?
4
Name: ________________________
ID: A
Problem
28. Consider the equation: 8 x  3  16 x  3
a) Solve this equation algebraically using logarithms.
b) Solve this equation using a different algebraic strategy.
c) Which strategy do you prefer? Explain why.
29. Use algebra to determine the x-intercept of the graph of y  4 log 2 x  12 .
30. Determine the exact value of x.
log 4 (x  5 )  log 4 (x  6 )  4
È ˘
È ˘
31. The pH of a solution can be described by the equation pH  log ÍÍÍÍ H + ˙˙˙˙ , where ÍÍÍÍ H + ˙˙˙˙ is the hydrogen-ion
Î ˚
Î ˚
concentration in moles/litre.
a) The hydrogen-ion concentration in a sample of watermelon is 5.0  10 6 moles/litre.
Determine the pH of the watermelon, to the nearest tenth.
b) A sample of lemon juice has a pH of 2.1.
Determine the hydrogen-ion concentration of the lemon juice, to four decimal places.
32. The Richter scale measures the intensity of an earthquake. The magnitude, M, of an earthquake can be
ÊÁ I ˆ˜
determined using the function M  log ÁÁÁÁ ˜˜˜˜ , where I microns is the intensity of the earthquake, and S microns
ËS ¯
is the intensity of a standard earthquake.
Determine the magnitude of an earthquake that is one-half as intense as an earthquake with magnitude 4.8.
Give the answer to the nearest tenth.
33. The decibel scale measures the intensity of sound. The loudness of a sound, L decibels (dB), can be
ÊÁ I ˆ˜
determined using the function L  10log ÁÁÁÁ ˜˜˜˜ , where I is the intensity of the sound and I 0 is the intensity of
ÁË I 0 ˜¯
the quietest sound that can be detected.
Determine the loudness of a sound, in decibels, that is one-third as intense as a sound with loudness
65 dB. Give the answer to the nearest whole number.
34. Two students each graduate with a student loan of $25 000 at 2.8% annual interest. Both students make
payments totalling $4056 per year. Student A makes payments of $338 per month, and the interest is
compounded every month. Student B makes payments of $156 every two weeks, and the interest is
compounded every two weeks. Compare the lengths of times it takes each student to repay the loan. Is one
payment plan significantly better than the other? Explain.
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