Free Printable Final Exam Review: Topic 6

1.

Select the equations that show exponential growth.

a)

$f\left(x\right)\ =3\left(1.01\right)^x$

b)

$f\left(x\right)=4000\left(0.95\right)^{x+1}$

c)

$f\left(x\right)=4^x$

d)

$f\left(x\right)=\ 0.5\left(3\right)^x$

e)

$f\left(x\right)=25\left(0.25\right)^x$

2.

Select the equations that show exponential decay.

a)

$f\left(x\right)\ =3\left(1.01\right)^x$

b)

$f\left(x\right)=4000\left(0.95\right)^{x+1}$

c)

$f\left(x\right)=4^x$

d)

$f\left(x\right)=\ 0.5\left(3\right)^x$

e)

$f\left(x\right)=25\left(0.25\right)^x$

3.

A population of 1500 deer decreases by 1.5% per year. At the end of 10 years, there will be approximately 1290 deer in the population. Which function can be used to determine the number of deer, y, in this population at the end of t years?

a)

$y=\ 1500\left(0.985\right)^t$

b)

$y=\ 1500\left(0.015\right)^t$

c)

$y=\ 1500\left(1.015\right)^t$

d)

$y=\ 1500\left(1.5\right)^t$

4.

There were 417 cell phones sold at an electronics store in January. Since then, cell phone sales at this store have increased at a rate of 3.75% per month. At this rate of growth, which function can be used to determine the monthly cell phone sales x months after January?

a)

f(x) = 417(3.75)^x

b)

f(x) = 417(0.0375)^x

c)

f(x) = 417(1.0375)^x

d)

f(x) = 417(1.375)^x

5.

Some banks charge a fee for a savings account that is left inactive for an extended period of time. The equation y = 5000(0.98)^x represents the amount remaining, y, of one account that was left inactive for a period of x years. What does the number 5000 represent in this situation?

a)

A fee charged for an inactive account

b)

The percent of money in the account after x years

c)

The amount of money in the account initially

d)

The amount of money in the account after x years

6.

a)

f(x) = 25(0.95)^x

b)

f(x) = 36(0.05)^x

c)

f(x) = 25(1.05)^x

d)

f(x) = 36(1.5)^x

7.

A child asks her dad for an allowance that starts with a penny and then doubles every day for a month. Which function can be used to model the amount of money, A, the child will receive each day, x?

a)

A(x) = 2(0.01)^x

b)

A(x) = 0.01(2)^x

c)

A(x) = 0.01(1 - 2)^x

d)

A(x) = 2(1.01)^x

8.

The function to find the value of a car after t years is given by v(t) = 24,000(.75)^t Which of the following statements is not true?

a)

The starting value of the car was $24,000.

b)

The y-values of the graph increase as the x-values increase.

c)

The value of b indicates this is an exponential decay situation.

d)

The horizontal asymptote is y = 0, which means the car will never have a value of $0.

9.

A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?

a)

14327

b)

4309

c)

839

d)

7680

10.

Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?

a)

$23,219.72

b)

$136.72

c)

$51,710.94

d)

$16,710.94

11.

What is the initial value for the function: f(x) = 300(1.16)^x?

a)

300

b)

1.16

c)

.16

d)

x

12.

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

a)

y=6(0.14)^x

b)

y=6(1+14)^x

c)

y=6(1.14)^x

d)

y=6(0.86)^x

13.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

14.

What is the range of this graph?

a)

y = 6

b)

(0, -3)

c)

y > -4

d)

y < -4

15.

What is the y-intercept of the function?

a)

2

b)

3

c)

1

d)

-2

16.

Suppose you deposit $3000 in a savings account that pays interest at an annual rate of 4%. What is the initial value?

a)

4%

b)

40%

c)

$3000(1.04)

d)

$3000

17.

What is the y-intercept?

a)

5

b)

1/3

c)

1

d)

0

18.

Which of the following statement about the graph of y=6(.5)^x is true?

a)

The equation of the asymptote is x=0.

b)

The coordinates of the y-intercept are (0,6)

c)

The graph includes the point (1.5, 2).

d)

The coordinates of the x-intercept are (.75, 0)

19.

Based on the graph, which statement does not appear to be true?

a)

The graph has a horizontal asymptote at y=0

b)

The y-intercept is at the point (0, 3)

c)

The graph represents exponential growth.

d)

The graph of the function shows a decrease over time.

20.

You borrowed $59,000 for 2 years at 11% which was compounded annually. What total will you pay back?

a)

$13,693.90

b)

$1,363.90

c)

$72,693.90

d)

$73,793.90

21.

Semi-Annually means how many times a year?

a)

4

b)

2

c)

1

d)

6

22.

Riley invested $1,000 in savings bonds. If the bonds earn 6.75% interest compounded semi-annually, how much total will Riley earn in 15 years?

a)

$1,584.62

b)

$2,651.39

c)

$2,706.86

d)

$1,825.10

23.

Olivia would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.

a)

$15,415.94

b)

$15,683.28

c)

$15,927.56

d)

$16,109.05

24.

Approximately what interest rate would be needed in order to grow an investment of $1,400 to $2,500 in 10 years if the interest was compound monthly?

a)

5.96%

b)

5.84%

c)

5.81%

d)

5.88%

25.

Given an investment of $1,500:
Which investment would have a larger balance after 5 years?
Option 1 - 4% compounded monthly
Option 2 - 3.9% compounded daily.

a)

Option 1

b)

Option 2

26.

Caiden earned $475 from mowing lawns last summer.He deposited this money in an account that pays an interest rate of 3.8% compounded annually. What will be his balance after 15 years?

a)

$827.52

b)

$831.10

c)

$839.45

d)

$846.80

27.

What does the P stand for in this formula?

a)

Initial amount

b)

Final amount

c)

Rate

d)

Time

e)

The number of times compounded per year

28.

What does the n stand for in this formula?

a)

Initial amount

b)

Final amount

c)

Rate

d)

Time

e)

The number of times compounded per year

29.

Maggie would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years?

a)

$15,415.94

b)

$15,683.28

c)

$15,927.56

d)

$16,109.05

30.

Approximately what interest rate would be needed in order to grow Christian's investment of $1400 to $2500 in 10 years if the interest was compound monthly?

a)

5.96%

b)

5.84%

c)

5.81%

d)

5.88%

31.

Treasure won $3,000 from a radio contest. If she puts this money in a bank account that earns 2.9% interest compounded quarterly, how much total will she earn in 10 years?

a)

$4915.59

b)

$3933.28

c)

$2979.81

d)

$4005.09

32.

What is the formula for continuously compounded interest?

a)

A = Pe^rt

b)

A = Pe^t

33.

Cora invested $400 at a rate of 35% for 8 months, compounded continuously. How much is her investment worth after 8 months?

a)

$520.07

b)

$505.12

c)

$460.11

d)

$7,643.74

34.

How long will it take $3000 to double if it is invested in an account that pays 3% compounded continuously?

a)

23.1 years

b)

22.1 years

c)

21.1 years

d)

20.1 years

35.

If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

a)

$1,225,54

b)

$2,225.54

c)

$22,255.40

d)

$225.54

36.

Andy invests $500 into an account with 4.8% interest, compounded monthly. How much will be in the account in 10 years?

a)

$799.06

b)

$520.36

c)

$807.26

d)

$877.61

37.

Mr. T invested $15,000 in an account that pays 5% interest compounding continuously, how much is in the account after 5 years?

a)

$15,500.50

b)

$19,260.38

c)

$19,260.40

d)

$21,500.25

38.

P = 26,000 | Rate = 2.4% | 4 years | Compounded Continuously | Amount owed???

a)

$2,496

b)

$28,496

c)

$3,406,924

d)

$28,619.74

39.

How much money will you have in 3 years if you invest $1025 in an account with 12% interest compounded continuously?

a)

$1114.76

b)

$1302.67

c)

$1392.45

d)

$1469.16

40.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

41.

Is the pictured graph growth, decay, or linear or none?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

42.

Is this exponential growth or decay?

a)

Growth

b)

Decay

43.

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

a)

y=6(0.14)^x

b)

y=6(1+14)^x

c)

y=6(1.14)^x

d)

y=6(0.86)^x

44.

A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?

a)

14327

b)

4309

c)

839

d)

7680

45.

Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?

a)

$23,219.72

b)

$136.72

c)

$51,710.94

d)

$16,710.94

46.

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?

a)

9766

b)

9006

c)

9765

d)

5433

47.

Twenty years ago, Mr. Davis purchased his home for $160,000. Since then, the value of the home has increased about 5% per year. How much is the home worth today?

a)

$176,783.29

b)

$424,527.63

c)

$57,357.75

d)

$532,041,076.80

48.

A stamp gets more expensive each year. It increases in value by 60 % each year. What is the growth FACTOR?

a)

.6

b)

1.06

c)

1.6

d)

.4

49.

Suppose you deposit $3000 in a savings account that pays interest at an annual rate of 4%. What is the growth factor?

a)

.96

b)

1.4

c)

1.04

d)

$3000

50.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

51.

Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?

a)

$23,219.72

b)

$136.72

c)

$51,710.94

d)

$16,710.94

52.

Since January 1980, the population of the city of Brownville has grown according to the mathematical model y=720,500(1.022)^x, where x is the number of years since January 1980. What is the was the population of Brownville in 1980?

a)

102.2 people

b)

720,500 people

c)

1.022 people

d)

1022 people

53.

Suppose you deposit $3000 in a savings account that pays interest at an annual rate of 4%. If no other money is added or withdrawn from the account, how much will be in the account after 10 years?

a)

$3122.18

b)

$4994.50

c)

$4440.73

d)

$86,776.40

54.

The attendance at the art museum at the New Year’s opening was 250 people. The attendance has been increasing at a rate of 3% each month. How many people will attend by the end of a year?

a)

356

b)

265

c)

5825

d)

1329

55.

In 1985, there were 285 cell phone subscribers in the small town of Centerville. The number of subscribers increased by 75% per year after 1985. How many cell phone subscribers were in Centerville in 1994?

a)

OVERFLOW

b)

1994

c)

1000

d)

43871

56.

You buy a new computer for $2100. The computer decreases by 50% annually. How much is it worth after 2 years.

a)

225

b)

325

c)

425

d)

525

57.

The population of Bloom Falls, Mass. (population 937) is slowly moving to a bigger city.
Every year the population drops by 4.5%. What is the population after 3 years?

a)

1,069 people

b)

894 people

c)

816 people

d)

854 people

58.

The city of Whoville has been much more stable since the Grinch turned his life around. The population of 900 is increasing at a rate of 7.5% per year. If the population continues growing at the same rate, how many people will there be in 11 years?

a)

424288

b)

1994

c)

10642

d)

900

59.

The Country of Puerto has 3,370,000 people in it and is decreasing at a rate of 4.5%. Estimate the population after 40 years.

a)

534,275

b)

19,601,148

c)

1,350,756

d)

2,521,541

60.

If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

a)

$1,225,54

b)

$2,225.54

c)

$22,255.40

d)

$225.54

61.

Change 32% into a decimal.

a)

32

b)

3.2

c)

.32

d)

.032

62.

Convert 70% to a decimal.

a)

.07

b)

.70

c)

.007

d)

.01

63.

Convert 3% to a decimal.

a)

.03

b)

.30

c)

.05

d)

.06

64.

Convert 3.5% to a decimal.

a)

3.5

b)

350

c)

.35

d)

.035

65.

Mr. T invested $15,000 in an account that pays 5% interest compounding continuously, how much is in the account after 5 years?

a)

$15,500.50

b)

$19,260.38

c)

$19,260.40

d)

$21,500.25

66.

How long would it take $7,000 to grow to $35,000 at 6% compounded continuously?

a)

27.6 years

b)

27.1 years

c)

26.0 years

d)

26.9 years

67.

Chelsea put $7500 into an account paying 5% compounded continuously. She now has $10,643.01. How long has the money been in the account?

a)

7 years

b)

6 years

c)

5 years

d)

4 years

68.

What does the A stand for in this formula?

a)

Initial Amount

b)

Final Amount

c)

Rate

d)

Time

e)

The number of times compounded per year

69.

What does the P stand for in this formula?

a)

Initial amount

b)

Final amount

c)

Rate

d)

Time

e)

The number of times compounded per year.

70.

Which formula is shown?

a)

Monthly compounded interest formula

b)

Annually compounded interest formula

c)

Continuously compounded interest formula

d)

Simple interest formula

71.

What does the r stand for in this formula?

a)

Rate as a percent

b)

Rate as a decimal

c)

number of times interest is compounded

72.

What does the t stand for in this formula?

a)

time in weeks

b)

time in months

c)

time in years

d)

the number of times interest is compounded per year

73.

When would we use this formula? A = Pe ^rt

a)

interest increases by fixed amount

b)

compound interest

c)

compound continuously

d)

decreases by fixed percent

74.

A student solves a problem about continuously compounded interest and determines that r = .3

a)

They should conclude that the interest rate is .3%

b)

They should conclude that the interest rate is 3%

c)

They should conclude that the interest rate is 30%

d)

They should conclude that the interest compounded for .3 years

75.

If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

a)

$1,225,54

b)

$2,225.54

c)

$22,255.40

d)

$225.54

76.

If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

a)

$1,225,54

b)

$2,225.54

c)

$22,255.40

d)

$225.54

77.

Mr. Thomas invested $15,000 in an account that pays 5% interest compounding continuously, how much is in the account after 5 years?

a)

$15,500.50

b)

$19,260.38

c)

$19,260.40

d)

$21,500.25

78.

If You Compounded Continuously an investment of $400 at a rate of 35% for 2 years

a)

$280

b)

$680

c)

$1,034.47

d)

$805.50

79.

Caiden earned $475 from mowing lawns last summer. He deposited this money in an account that pays an interest rate of 3.8% compounded continuously. What will be his balance after 15 year?

a)

$827.52

b)

$839.93

c)

$839.45

d)

$846.80

80.

log(x+6) = 1

a)

4

b)

4.222

c)

-5

d)

-9.550

81.

Evaluate.

log₂32=3x

a)

5/3

b)

3/5

c)

5

d)

3

82.

log_x1000=3

a)

1

b)

10

c)

30

d)

3

83.

log₂(x+3)=4

a)

16

b)

13

c)

3

d)

10

84.

Solve for x:
log_x25 = 2

a)

5

b)

-5

c)

1/5

d)

-1/5

85.

Convert log(x) = 5 to exponential form

a)

1⁵=x

b)

10^x=5

c)

x⁵=10

d)

10⁵=x

86.

Convert 6^(x+2)=216 to logarithmic form

a)

log₂₁₆(x+2)=6

b)

log₆(x+2)=216

c)

log₆(216)=x+2

d)

log_(x+2)(216)=6

87.

Solve for x.
log_x(64)=3

a)

x=8

b)

x=4

c)

x=3

d)

x=64

88.

Solve for x
5^x = 17

a)

x = log₁₇5

b)

x = log 5 + log 17

c)

x = log₅17

d)

x = (log 5)/(log 17)

89.

Write in exponential form.
log₂(¹/₈) = -3

a)

2^-3 = ¹/₈

b)

2^1/8= -3

c)

-3² = ¹/₈

d)

-3^1/8 = 2

90.

Evaluate the following logarithm:

log₄16

a)

1

b)

-2

c)

2

d)

¹/₂

91.

Evaluate the following logarithm:

log₅5

a)

1

b)

0

c)

-1

d)

¹/₂

92.

Evaluate the following logarithm:

log₃27

a)

3

b)

2

c)

-3

d)

¹/₃

93.

Rewrite in exponential form:
log (x) = ¼

a)

x^1/4 = 1

b)

1^x=¼

c)

10^1/4 = x

d)

10^x = ¼

94.

Rewrite in exponential form:
ln(2) = x

a)

2^x= 10

b)

10² = x

c)

e^x= 2

d)

e² = x

95.

What is the value of ln(e⁷)

a)

2.718...

b)

1

c)

7

d)

Does not exist

96.

Solve for x:

e^2x = 11

a)

x = (ln 11)/2

b)

x = 2log_e11

c)

x = 2e(log11)

d)

x = ln (11/2)

97.

log_x1000 = 3

a)

1

b)

10

c)

30

d)

3

98.

Solve for x:
4²^x+ 1 = 17

a)

x = 1

b)

x = -1

c)

x = 2

d)

x = -2

99.

Solve for x:

2^{3x - 1} = 32

a)

0

b)

-1

c)

5/3

d)

2

100.

Solve: 7^-x = 49

a)

x = 1

b)

x = -1

c)

x = 2

d)

x = -2

101.

Logarithms and Exponentials are _______________?

a)

parallel

b)

perpendiular

c)

inverses

d)

congurent

102.

Rewrite log_vn = a in exponential form.

a)

v^a = n

b)

n^a = v

c)

vⁿ = a

d)

aⁿ = v

103.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

104.

Solve for x.
5^x = 1

a)

0

b)

-1

c)

2

d)

1

105.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

106.

Log with a base "e" (log_e) is the same thing as...

a)

"e"

b)

natural logarithm (ln)

c)

common logarithm (log)

d)

natural log, base "e" ln_e

107.

Change to Logarithmic Form:
5³ = 125

a)

log ₅ 125 = 3

b)

log₃125 = 5

c)

log ₅ 3 =125

d)

log₁₂₅ 3 = 5

108.

Solve for x:
4²^x+ 1 = 17

a)

x = 1

b)

x = -1

c)

x = 2

d)

x = -2

109.

log₈(1/2) = x

a)

-1/3

b)

1/3

c)

1/2

d)

-1/2

110.

log₆(2x + 3) = 3

a)

x = 106.5

b)

x = 100

c)

x = 16

d)

x = 50

111.

Solve for x.

log_x100 = 2

a)

10

b)

50

c)

10,000

d)

0.02

112.

a)

0.0005

b)

5.5

c)

121

d)

3.32

113.

a)

-2

b)

2

c)

4

d)

-4

114.

Solve for x.

log₆x = 3

a)

2

b)

729

c)

216

d)

18

115.

Solve for x.

log₃12 = x

a)

2.262

b)

0.442

c)

4

d)

1.401

116.

Evaluate the logarithmic expression without a calculator:

\log_{10}10,000

a)

1000

b)

4

c)

3

d)

5

117.

Evaluate the logarithmic expression without a calculator:

\log_{20}1

a)

0

b)

20

c)

1

d)

10

118.

The natural logarithm is represented as what?

a)

log

b)

ln

119.

The natural logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

120.

Solve: 2^x = 25

Round to the nearest hundredth.

a)

x = 4.64

b)

x = 4.65

c)

x = 1.40

d)

x = 1.10

121.

Solve: 9^x-8 = 70

Round to the nearest hundredth.

a)

x = 9.93

b)

x = 1.93

c)

x = 1.85

d)

x = 9.85

122.

The base of common log is 10. So log 100 = ?

a)

1

b)

2

c)

10

d)

50

123.

Evaluate.

log1000

a)

1

b)

2

c)

3

d)

4

124.

Evaluate.

log 0.1

a)

-2

b)

-1

c)

1

d)

2

125.

Evaluate.

log 1

a)

-2

b)

-1

c)

0

d)

1

126.

Use a calculator to evaluate log 25

a)

1.398

b)

1.598

c)

-1.397

d)

0.80

127.

lnx = -3

a)

8.1548

b)

-8.1548

c)

0.0498

d)

-0.0498

128.

Evaluate.

log₅25

a)

2

b)

5

c)

25

d)

125

129.

Evaluate:
log₄16

a)

2

b)

4

c)

1/2

d)

-2

130.

Evaluate.

log₄1 =

a)

0

b)

1

c)

4

d)

Undefined

131.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

132.

Evaluate.
log₆(¹/₂₁₆)

a)

3

b)

¹/₃

c)

-¹/₃

d)

-3

133.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

134.

Write in exponential form.
log₂(¹/₈) = -3

a)

2^-3 = ¹/₈

b)

2^1/8= -3

c)

-3² = ¹/₈

d)

-3^1/8 = 2

135.

Write in logarithmic form.
5² = 25

a)

log₅2 = 25

b)

log₂25 = 5

c)

log₂₅5 = 2

d)

log₅25 = 2

136.

Write in logarithmic form.
2^-4 = ¹/₁₆

a)

log₂(¹/₁₆) = -4

b)

log_-4(¹/₁₆) = 2

c)

log_-4 2 = ¹/₁₆

d)

log₂(-4) = ¹/₁₆

137.

Rewrite log₂8 = 3 in exponential form

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

138.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

139.

Rewrite e^x = 9 using a logarithm

a)

ln x = 9

b)

ln 9 = x

c)

log_x e = 9

d)

log₉ x = e

140.

Solve the equation for x.

a)

32

b)

25

c)

1.66

d)

512

141.

Solve

14^4-6x= 11

(round to the nearest tenth)

a)

5

b)

0.5

c)

0.1

d)

1

142.

What is the inverse of

c\left(x\right)=\log\left(x\right)

a)

$c^{-1}\left(x\right)=x^e$

b)

$c^{-1}\left(x\right)=\ln x$

c)

$c^{-1}\left(x\right)=x^{10}$

d)

$c^{-1}\left(x\right)=10^x$

143.

What is the inverse of

n\left(x\right)=\ln\left(x\right)

a)

$n^{-1}\left(x\right)=\log e$

b)

$n^{-1}\left(x\right)=x^e$

c)

$n^{-1}\left(x\right)=e^x$

d)

$n^{-1}\left(x\right)=x^{\ln}$

144.

Find the inverse of y=9^x

a)

y=log_x9

b)

y=log₁₀9

c)

x=log_y9

d)

y=log₉x

145.

Find the Inverse of $y\ =\ \log_4\left(x-1\right)$

a)

$y=x$

b)

$y=\log_34^x$

c)

$y=4^x+1$

d)

$y=4^{x+1}$

146.

Find the inverse of $y=\ln\left(x+3\right)$

a)

$y=e^x-3$

b)

$y=e^{x-3}$

c)

$y=e^x+3$

d)

$y=e^{x+3}$

147.

What are the inverse points for the coordinates:

(3, 0) , (2, -4), (5, 5) and (-6,8)

a)

(3,0) , (2, -4) , (5,5) , (6,8)

b)

(0,3) , (-4,2) , (5,5) , (8,-6)

c)

(3,2), (0, -4), (5, -6), (5,8)

148.

Find the inverse of $f(x)=10+7x$

a)

$f^{-1}(x)=\frac{x-7}{10}$

b)

$f^{-1}(x)=\frac{x-10}{7}$

c)

$f^{-1}(x)=\frac{1}{10+7x}$

149.

The inverse of the function f(x) is written as ...

a)

f ^-1(x)

b)

f ²(x)

c)

f '(x)

d)

f ⁺(x)

150.

Find the inverse of $f\left(x\right)=\frac{1}{4}x-7$

a)

f^-1(x) = 4x + 7

b)

f^-1(x) = -4x+28

c)

f^-1(x) = -4x - 7

d)

f^-1(x) = 4x+28

151.

Is the inverse function found correctly?

a)

yes

b)

no

152.

What does it mean to find the inverse of a function?

a)

the x's and y's are switched

b)

the x's and y's are divided by 2

c)

the x's and y's are made negative

d)

the x's and y's are the same

153.

What is the inverse of the points
(1,3)(2,4)(6,8)

a)

(3,1)(4,2)(8,6)

b)

(-3,-1)(-4,-2)(-8,-6)

c)

(1,3)(2,4)(6,8)

d)

(-1,-3)(-2,-4)(-6,-8)

154.

Find the inverse of y=9^x

a)

y=log_x9

b)

y=log₁₀9

c)

x=log_y9

d)

y=log₉x

155.

Write log_b(xy) as two logs

a)

log_bx+log_by

b)

log_bx-log_by

c)

log_bx*log_by

d)

log_bx/log_by

156.

Write log_b(x/y) as two logs

a)

log_bx-log_by

b)

log_bx+log_by

c)

log_bx*log_by

d)

log_bx/log_by

157.

Rewrite log_b(xⁿ)

a)

nlog_bx

b)

(log_bx)ⁿ

c)

xⁿlog_bx

d)

log_b(xⁿ)

158.

Write the expression as a single logarithm. Then simplify if possible.
log₅3 + log₅6 + log₅9

a)

log₅69

b)

log₅56

c)

log₅162

d)

log₅98

159.

Write the expression as a single logarithm. Then simplify if possible.
log 6 - log 3 + 2 log 7

a)

log 98

b)

log 78

c)

log 56

d)

log 45

160.

a)

6log₈(xyz)

b)

log₈(x) - log₈(y) - 6log₈(z)

c)

log₈(x) + log₈(y) - log₈(z)

d)

log₈(x) + log₈(y) + 6log₈(z)

161.

a)

log (a⁵+ b²⁵)

b)

log (a⁵− b²⁵)

c)

log (ab²⁵)

d)

log (a⁵/b²⁵)

162.

a)

2ln(x) + ln(y)

b)

4ln(x) + 2ln(y)

c)

2ln(x) - 2ln(y)

d)

4ln(xy)

163.

Write as a single log: log 12 + 2 log x

a)

log (12 + 2x)

b)

log (14x)

c)

log (12 * 2x)

d)

log (12x²)

164.

Condense this expression to a single logarithm.

a)

b)

c)

d)

165.

Which of the following is a possible expansion for this logarithm? $\log_324$
Check all that apply.

a)

$\log_34+\log_320$

b)

$\log_310+\log_314$

c)

$\log_34+\log_36$

d)

$\log_348-\log_32$

e)

$\log_38+\log_33$

166.

Express as a single logarithm.
$\log_39\ +\log_327\ =\ \log_3\left(?\right)$
(Type a NUMBER for the ?)

(a)

167.

Express as a single logarithm & simplify
$\log_28\ -\log_216$

a)

$\log_4128\ =\ \frac{7}{2}$

b)

$\log_2\left(\frac{1}{2}\right)=-1$

c)

$\frac{\log_28}{\log_216}=\frac{3}{4}$

d)

$\log_2\left(-8\right)=-4$

168.

Which expression(s) are equivalent to
$\log_412$ ?
Select all that apply.

a)

$\frac{\log12}{\log4}$

b)

$\log_42+\log_46$

c)

$\log_436-\log_43$

d)

$\log_41-\log_412$

169.

Solve the equation.
$\log x-\log4=1$

a)

125

b)

40

c)

25

d)

20

170.

What is the value of ln(e⁷)

a)

2.718...

b)

1

c)

7

d)

Does not exist

171.

Solve for x:

e^2x = 11

a)

x = (ln 11)/2

b)

x = 2log_e11

c)

x = 2e(log11)

d)

x = ln (11/2)

172.

Solve for x:
4²^x+ 1 = 17

a)

x = 1

b)

x = -1

c)

x = 2

d)

x = -2

173.

Solve for x:

2^{3x - 1} = 32

a)

0

b)

-1

c)

5/3

d)

2

174.

log₂(x + 2) + log₂x = 3

a)

-4, 2

b)

-2, 4

c)

2

d)

1

175.

Rewrite in exponential form:
log (x) = ¼

a)

x^1/4 = 1

b)

1^x=¼

c)

10^1/4 = x

d)

10^x = ¼

176.

Rewrite in exponential form:
ln(2) = x

a)

2^x= 10

b)

10² = x

c)

e^x= 2

d)

e² = x

177.

Solve the equation.
$\log x-\log4=1$

a)

125

b)

40

c)

25

d)

20

178.

What is the value of ln(e⁷)

a)

2.718...

b)

1

c)

7

d)

Does not exist

179.

Solve the following equation for x. Round your solution to two decimal places.

ln(2x) - ln(41) = 2

a)

x = 0.36

b)

x = 151.48

c)

x = 41

d)

None of these are solutions

180.

Solve for x:

e^2x = 11

a)

x = (ln 11)/2

b)

x = 2log_e11

c)

x = 2e(log11)

d)

x = ln (11/2)

181.

log₂32=3x

a)

5/3

b)

3/5

c)

5

d)

3

182.

log₄(3x-1)=log₄(2x+3)

a)

4

b)

3

c)

1

d)

8

183.

log_x1000=3

a)

1

b)

10

c)

30

d)

3

184.

log₈(4x+4)=2

a)

15

b)

12

c)

10

d)

3

185.

lnx = -3

a)

8.1548

b)

-8.1548

c)

0.0498

d)

-0.0498

186.

Solve for x:
4²^x+ 1 = 17

a)

x = 1

b)

x = -1

c)

x = 2

d)

x = -2

187.

Solve for x:

2^{3x - 1} = 32

a)

0

b)

-1

c)

5/3

d)

2

188.

Solve:
_{log (4x − 5) = log (2x − 1)}

a)

0

b)

1

c)

2

d)

3

189.

Solve: 9^8-x = 27^x-3

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

190.

Solve: 7^-x = 49

a)

x = 1

b)

x = -1

c)

x = 2

d)

x = -2

191.

Solve: 2^x = 4^x+1

a)

x = -2

b)

x = 2

c)

x = -3

d)

x = 3

192.

Solve log(x) + log(x+3) = 1

a)

5

b)

-2

c)

-5

d)

2

193.

log₂(x + 2) + log₂x = 3

a)

-4, 2

b)

-2, 4

c)

2

d)

1

194.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

195.

Condense the Logarithm $5\log_{ }a\ -\ 25\log_{ }b$

a)

$\log\ \left(a^5+b^{25}\right)$

b)

$\log\ \left(a^5-b^{25}\right)$

c)

$\log\ \left(ab\right)^{25}$

d)

$\log_{ }\ \left(\frac{a^5}{b^{25}}\right)$

196.

Condense $3\log_{ }x+4\log_{ }y\ +\log_{ }z$

a)

$\log_{ }\ x^3y^4z$

b)

$12\log_{ }\ xyz$

c)

$\log_{ }\ 3x4yz$

d)

logx³y³z³

197.

Use the change-of-base formula to evaluate $\log_211$

a)

$3.459$

b)

$4.359$

c)

$5.123$

d)

2.345

198.

Simplify: $\log_4\left(x+4\right)-\log_4\left(x-5\right)$

a)

$\log_49$

b)

$\log_4\left(2x-1\right)$

c)

$\log_4\left(x^2-x-20\right)$

d)

$\log_4\left(\frac{x+4}{x-5}\right)$

199.

Simplify: $2\log_3\left(11x\right)$

a)

$\log_3\left(22x\right)$

b)

$\log_3\left(121x\right)$

c)

$\log_3\left(121x^2\right)$

d)

$\log_3\left(11x^2\right)$

200.

Simplify: $\frac{1}{4}\log_516+3\log_5x$

a)

$\log_5\left(4x^3\right)$

b)

$\log_5\left(2x^3\right)$

c)

$\log_5\left(6x\right)$

d)

$\log_5\left(\frac{2}{x^3}\right)$

201.

Simplify: $\frac{1}{4}\log_281+\frac{1}{2}\log_249$

a)

$\log_221$

b)

$\log_210$

c)

$\log_2\left(\frac{3}{7}\right)$

d)

$\log_244.75$

202.

Simplify: $\frac{1}{2}\log_964+\log_9x$

a)

$\log_9\left(32x\right)$

b)

$\log_9\left(8x\right)$

c)

$\log_9\left(\frac{8}{x}\right)$

d)

$\log_98x$

203.

Write the expression as a single logarithm. Then simplify if possible.
log 6 - log 3 + 2 log 7

a)

log 98

b)

log 78

c)

log 56

d)

log 45

204.

Expand using the properties of Logaritms $\log_{ }\ \frac{x^3}{y^4z}$

a)

$\log_{ }x+4\log_{ }y\ +\log_{ }z$

b)

$3\log_{ }x-4\log_{ }y\ -\log_{ }z$

c)

$3\log_{ }x+4\log_{ }y\ +\log_{ }z$

d)

$3\log_{ }x-4\log_{ }y\ +\log_{ }z$

205.

Use these and other properties of logarithms to evaluate the expression.

$\log_232\ -\ 6^{\log_63}$

a)

$2$

b)

$-2$

c)

$8$

d)

$3$

206.

Expand the logarithm.
$\log_4\sqrt{x^3y}$

a)

$\frac{1}{2}\log_4\left(x\right)-\frac{1}{2}\log_4\left(y\right)$

b)

$\frac{3}{2}\log_4\left(x\right)-\frac{1}{2}\log_4\left(y\right)$

c)

$\frac{1}{2}\log_4\left(x\right)-\log_4\left(y\right)$

d)

$\frac{3}{2}\log_4\left(x\right)-\log_4\left(y\right)$

207.

Use the change-of-base formula to evaluate $\log_7\ \frac{3}{16}$ rounded to two decimal places

a)

$0.82$

b)

$0.86$

c)

$0.85$

d)

$0.87$

208.

Expand the logarithm.
$\log\frac{x}{y^6}$

a)

$\log x+6\log y$

b)

$\log x-6\log y$

c)

$\log x+\log6y$

d)

$\log x-\log6y$

209.

Expand . $\log_6\left(\frac{5x^3}{y}\right)$

a)

$\log_65x^3-\log_6y$

b)

$\log_65+\log_6x^3-\log_6y$

c)

$\log_65+3\log_6x-\log_6y$

d)

$\log_65+3\log_6x+\log_6y$

210.

Which property of logarithms is demonstrated below:

\log_920\ =\ \frac{\log20}{\log9}

a)

Product property

b)

Quotient property

c)

Power property

d)

Change of Base Property

211.

Rewrite as a single logarithm:

\log3\ +\ \log7

a)

log 10

b)

log 21

c)

log 3/7

d)

log 3/log 7

212.

Rewrite as a single logarithm:

\log_260\ -\ \log_210

a)

$\log_26$

b)

$\log_250$

c)

$\frac{\log_260}{\log_210}$

d)

$\log_270$

213.

Use the properties of logarithms to rewrite as the sum of two logarithms:

\log55

a)

log 40 + log 15

b)

log 50 + log 5

c)

log 11 + log 5

214.

Use the properties of logarithms to rewrite as the difference of two logs:

\log_545

a)

$\log_590\ -\log_52$

b)

$\log_515-\log_53$

c)

$\frac{\log45}{\log\ 5}$

d)

$\log_550-\log_55$

215.

Which of the logarithms below is equivalent to the following:
$2\log12$

a)

log 10

b)

log 6

c)

log 24

d)

log 144

216.

Use the change of base rule to simplify. Round your answer to the nearest thousandth:

\log_420

(a)

217.

Use the change of base property to rewrite as a single logarithm:

$\frac{\log15}{\log3}$

a)

$\log\ \frac{1}{5}$

b)

$\log5$

c)

$\log_{15}3$

d)

$\log_315$

218.

True or False:

log 12 - log 4 = log 8

a)

True

b)

False

219.

$-2\log3=\log\frac{1}{9}$

True or False:

a)

True

b)

False

220.

$\frac{\log7}{\log\ 20}=\log\ \left(\frac{7}{20}\right)$

True or False:

a)

True

b)

False

221.

Solve for x:

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

222.

Solve for x:

log₄(3x-1)=log₄(2x+3)

a)

4

b)

3

c)

1

d)

8

223.

Solve for x:

log₂(x+3)=4

a)

16

b)

13

c)

3

d)

10

224.

Solve for x:

log₈(4x+4)=2

a)

15

b)

12

c)

10

d)

3

225.

Solve for x:

log_x1000=3

a)

1

b)

10

c)

30

d)

3

226.

Solve for x:

log₅ (x + 3) = log₅ x + log₅ 3

a)

3/2

b)

9/2

c)

2/3

d)

No Solution

227.

Using a calculator, solve for x:

2.8^x = 41

a)

0.277

b)

3.607

c)

-0.282

d)

3.684

228.

Solve for x:

log₂(2) + log₂(8x) = 6

a)

x = 3

b)

x = 2

c)

x = 6

d)

x = 4

229.

Solve for x:

log(x+6) = 1

a)

4

b)

4.222

c)

-5

d)

-9.550

Final Exam Review: Topic 6

Total questions: 229

Worksheet time: 19hrs 28mins

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