Free Printable Unit 9 Retake Exponential and Logarithmic Functions

1.

solve for x.

$2^x=2^{3x-4}$

a)

2

b)

-2

c)

1/2

d)

4/3

2.

solve for x.

$25^{x+3}=5^{5x-9}$

a)

1

b)

4

c)

5

d)

3

3.

Solve for p:
4^p+2 = 64

a)

-16/9

b)

1

c)

8

d)

7/6

4.

To solve an exponential equation, the (a) must be the same!

5.

Rewrite

\frac{1}{36}

as a power of 6.

a)

6

b)

$6^2$

c)

$6^6$

d)

$6^{-2}$

6.

Rewrite 1000 as a power of 10:

a)

$10^3$

b)

$10^2$

c)

$10^{10}$

d)

10

7.

Solve the following exponential equation:
$9^{8-x}=27^{x-3}$

a)

$x=5$

b)

$x=-5$

c)

$x=\frac{1}{5}$

d)

$x=-\frac{1}{5}$

8.

Solve the following exponential equation:
$\left(\frac{1}{2}\right)^{2x}=4^3$

a)

$x=3$

b)

$x=-\frac{5}{2}$

c)

$x=-3$

d)

$x=\frac{5}{2}$

9.

3² = 9

a)

log ₃ 2 = 9

b)

log ₉ 3 = 2

c)

log ₃ 9 = 2

d)

log ₂ 9 = 3

10.

2⁵ = 32

a)

log ₅ 32 = 2

b)

log ₂ 32 = 5

c)

log ₃₂ 5 = 2

d)

log ₂ 5 = 32

11.

b^k = m

a)

log _b m = k

b)

log _m k = b

c)

log _b k = m

d)

log _k m = b

12.

e³ = 20.1

a)

ln 20.1 = e

b)

ln 3 = 20.1

c)

ln e = 20.1

d)

ln 20.1 = 3

13.

10³ = 1000

a)

log ₁₀₀₀ 3 = 10

b)

log ₃10 = 1000

c)

log 3 = 1000

d)

log 1000 = 3

14.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

15.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

16.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

17.

Rewrite this equation in logarithmic form.

a)

b)

c)

d)

18.

e³ = 20.1

a)

ln 20.1 = e

b)

ln 3 = 20.1

c)

ln e = 20.1

d)

ln 20.1 = 3

19.

Expand: $\log_6\left(\frac{5}{4y}\right)$

a)

$\log_65\ +\ \log_64\ +\ \log_6y$

b)

$\log_65\ -\ \log_64\ +\ \log_6y$

c)

$\log_65\ -\ \log_64\ -\ \log_6y$

d)

$\log_65\ -\ \log_64y$

20.

Expand: $\log_4\left(3x^2\right)$

a)

$2\log_43x$

b)

$2\log_43\ +\ 2\log_4x$

c)

$\log_43\ +\ 2\log_4x$

d)

$2\log_43\ +\ \log_4x$

21.

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)

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

22.

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

a)

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

b)

$12\log_{ }\ xyz$

c)

$\log_{ }\ 3x4yz$

d)

logx³y³z³

23.

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)

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

24.

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)

$\log_98x$

25.

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)

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

26.

log(2x) - log(5) = log(30)

a)

6/5

b)

45/2

c)

75

d)

-3/8

27.

log(4x) - log(4) = log(12)

a)

12

b)

4

c)

10

d)

100

28.

Solve

a)

8

b)

-8

c)

1/8

d)

-1/8

29.

a)

5

b)

13

c)

84

d)

-20

30.

Solve

a)

A

b)

B

c)

C

d)

D

31.

$\ln\left(-2x\right)+\ln\left(4\right)=5$

Solve the equation for the missing variable. Be sure to check for extraneous solutions.

a)

n = -12.34

b)

n = -18.55

c)

n = -4.65

d)

n = 5.23

32.

$\ln\left(8\right)+\ln\left(x+9\right)=4$

Solve the equation for the missing variable. Be sure to check for extraneous solutions.

a)

x = 4.25

b)

x = -3.34

c)

x = 6.52

d)

x = -2.18

33.

$\ln\left(x-2\right)+\ln\left(9\right)=\ln\left(66\right)$

Solve the equation for the missing variable. Be sure to check for extraneous solutions.

a)

x = 9.33

b)

x = 8.54

c)

x = 12.35

d)

x = 17.23

34.

$-3\cdot e^{2m-5}-7=-34$

Solve the equation for the missing variable. Be sure to check for extraneous solutions.

a)

m = 2.4

b)

m = 9.2

c)

m = 3.6

d)

m = 4.8

35.

$e^{a+1}=65$

Solve the equation for the missing variable. Be sure to check for extraneous solutions.

a)

a = 2.94

b)

a = 3.17

c)

a = 1.42

d)

a = 0.89

36.

The number of turkey vultures in a nature sanctuary is doubling each year. When the sanctuary opened, it was home to 204 turkey vultures. Which equation can be used to find the number of turkey vultures after x years?

a)

$y=204\left(x\right)^2$

b)

$y=2\left(204\right)^x$

c)

$y=204\left(2\right)^x$

d)

$y=x\left(2\right)^{204}$

37.

A population of ants increases by a factor of 5 each year. Initially there were 450 aunts. Which equation represents the amount of aunts after 9 years?

Let y represent the total amount of aunts after x years.

a)

$y=450\left(9\right)^5$

b)

$y=450\left(5\right)^9$

c)

$y=5\left(450\right)^9$

d)

$y=9\left(450\right)^5$

38.

You have inherited land that was purchased for $30,000 in 1960. The value of the land increased by approximately 5% per year. Write an equation to represent the situation:

a)

$f\left(x\right)\ =\ 30,000\left(1\ +\ 0.05\right)^t$

b)

$f\left(x\right)\ =\ 30,000\left(1\ -\ 0.05\right)^t$

39.

Is y = 54(.20)^x growth or decay?

a)

Growth because of the 54

b)

Decay because of the .20

c)

Decay because of the 54

d)

Growth because of the .20

40.

The population of Winnemucca, Nevada, can be modeled by P=6191(1.04)^t where t is the number of years since 1990. What percent did the population increase each year?

a)

104%

b)

4%

c)

40%

d)

400%

41.

A sailboat that costs $5,950 decreases in value by 11% per year. How much will the boat be worth after 6 years?

a)

$5,884.00

b)

$5,178.97

c)

$2,992.96

d)

$2,957.04

42.

You bought a brand new car for $45,000. The car depreciates at approximately 7% per year. How much will the car be worth after 8 years? Round to the nearest whole dollar.

a)

$77,318

b)

$25,181

c)

$41,850

d)

The value won't change at all.

43.

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)

9765

b)

9006

c)

5433

d)

9766

44.

You buy a new computer for $2100. The computer decreases by 50% annually. When will the computer have a value of $600?

a)

between 1 and two years

b)

more than 5 years

c)

less than a year

d)

between 3 and 4 years

45.

You drink a beverage with 120 mg of caffeine. Each hour, the caffeine in your system decreases by about 12%. How long until you have 10mg of caffeine?

a)

19 to 20 hours

b)

10 to 20 hours

c)

15 to 16 hours

d)

5 to 6 hours

46.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?

a)

y=8(15,000)^x

b)

y=15,000(1.08)^x

c)

y=15,000(0.92)^x

d)

y=15,000(0.08)^x

47.

Is this exponential growth or decay?

a)

Growth because a=1

b)

Growth because there is no a

c)

Decay because b=0.5

d)

Neither because a=0

48.

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

49.

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

50.

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

51.

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

52.

The poplulation of Eden is growing continuously at a rate of 1.9%. If the current population is 15,230, about how many years to reach 20,000?

a)

31

b)

2

c)

15

d)

68

53.

Which of these circumstances would require the formula A=Pe^rt ?

a)

Daily

b)

Monthly

c)

Quarterly

d)

Continuously

54.

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

55.

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

56.

Select all expressions that are equal to log₂ 8.

a)

log₃ 27

b)

log₁₀ 1,000

c)

log₅ 20

d)

log₅ 125

e)

log₁₀ 100

57.

Write an equivalent equation in logarithmic form: $10^0$ = ___.

a)

$\log_110$ =0

b)

$\log_{10}1=0$

c)

$\log_{10}1=10$

d)

$\log_{10}10=1$

58.

log ₉ 27 =

a)

3

b)

2/3

c)

3/2

d)

1/3

59.

log (1/10,000)

a)

1/4

b)

-4

c)

1000

d)

-1000

60.

log ₂₅(1/125)

a)

-1/5

b)

5

c)

-3/2

d)

2/3

61.

log ₃₂ 4 =

a)

1/8

b)

8

c)

5/2

d)

2/5

62.

log ₁₇ 1

a)

1

b)

0

c)

17

d)

18

Unit 9 Retake Exponential and Logarithmic Functions

Total questions: 62

Worksheet time: 6hrs 57mins

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