Free Printable Exponential and Logarithm Test Review

1.

Rewrite in exponential form:

log₃(9)=2.

a)

3⁹=2

b)

3²=9

c)

x²=9

d)

3^x=2

2.

Rewrite in logarithmic form:

6² = 36

a)

log₆ 2 = 36

b)

log₆ 36 = 2

c)

ln 36 = 2

d)

6³⁶ = 2

3.

Rewrite in logarithmic form:

5³ = 125

a)

log ₅ 125 = 3

b)

log₃125 = 5

c)

log ₅ 3 =125

d)

log₁₂₅ 3 = 5

4.

Rewrite in exponential form:

log₂ 0.25 = -2

a)

-2²= 0.25

b)

-2^0.25= 2

c)

2^-2= 0.25

d)

No correct answer

5.

Rewrite in logarithmic form:

3⁴ = 81

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

6.

log ₃9 =

a)

1/2

b)

2

c)

1/3

d)

3

7.

log ₂₅ 5 =

a)

1/2

b)

2

c)

1/5

d)

5

8.

log ₉ (1/3) =

a)

-1/2

b)

-2

c)

-3

d)

-1/3

9.

log ₂16 =

a)

3

b)

2

c)

4

d)

5

10.

log ₁₇ 1 =

a)

1

b)

0

c)

17

d)

18

11.

log ₃ 27 =

a)

4

b)

2

c)

5

d)

3

12.

Convert to exponential form: $\log_8\left(\frac{1}{64}\right)=-2$

a)

$-2^8=\frac{1}{64}$

b)

$\left(\frac{1}{64}\right)^{-2}=8$

c)

$8^{-2}=\frac{1}{64}$

d)

$\left(\frac{1}{64}\right)^8=-2$

13.

Convert to exponential form: $\log_{17}289=2$

a)

$17^2=289$

b)

$289^2=17$

c)

$17^{289}=2$

d)

$2^{17}=289$

14.

Convert to exponential form: $\log_71=0$

a)

$1^0=7$

b)

$7^0=1$

c)

$7^1=0$

d)

$0^7=1$

15.

Convert to exponential form: $\log_55=1$

a)

$1^5=5$

b)

$5^5=1$

c)

$5^1=5$

d)

$5^5=5$

16.

Convert to exponential form: $\log_2x=16$

a)

$2^x=16$

b)

$x^2=16$

c)

$16^2=x$

d)

$2^{16}=x$

17.

Convert to logarithmic form: $2^9=512$

a)

$\log_9512=2$

b)

$\log_2512=9$

c)

$\log_29=512$

d)

$\log_92=512$

18.

Convert to logarithmic form: $6^{-3}=\frac{1}{216}$

a)

$\log_6\left(\frac{1}{216}\right)=-3$

b)

$\log_3216=-6$

c)

$\log_6-3=\frac{1}{216}$

d)

$\log_{ }\left(\frac{1}{216}\right)=6$

19.

Convert to logarithmic form: $11^0=1$

a)

$\log_01=11$

b)

$\log_011=1$

c)

$\log_{ }11=1$

d)

$\log_{11}1=0$

20.

Convert to logarithmic form: $6^1=6$

a)

$\log_66=1$

b)

$\log_{ }6=6$

c)

$\log_16=6$

d)

$\log_61=6$

21.

Convert to logarithmic form: $3^x=27$

a)

$\log_x27=3$

b)

$\log_3x=27$

c)

$\log_327=x$

d)

$\log_{27}x=3$

22.

Sovle for x:
5^{-3x - 1} = 25

a)

x = -1

b)

x = -4

c)

x = -3

d)

x = 1

23.

Solve 3³ = 3^{4x + 2}

a)

x = ¼

b)

x = -¼

c)

x = ½

d)

x = -½

24.

Solve: 7^-x = 49

a)

x = 1

b)

x = -1

c)

x = 2

d)

x = -2

25.

Sovle for x:
5^{-3x - 1} = 25

a)

x = -1

b)

x = -4

c)

x = -3

d)

x = 1

26.

Solve 3³ = 3^{4x + 2}

a)

x = ¼

b)

x = -¼

c)

x = ½

d)

x = -½

27.

Solve 8 = 2^5x+7

a)

x = ⅘

b)

x = ¼

c)

x = -⅘

d)

x = -¼

28.

8^3x+3 = 8⁶

a)

x=28

b)

x=3

c)

x=1

d)

x=12

29.

Solve each equation. Select the closest answer.

a)

4.5

b)

1.5

c)

1.8

d)

5

30.

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

31.

Solve the equation for x.

a)

5.352

b)

4.326 E91

c)

2.324

d)

1.89

32.

What exponent makes this equation true?

8^x=64

(a)

33.

What exponent makes this equation true?

3^x=27

(a)

34.

What exponent makes this equation true?

4^x=4^5

(a)

35.

Solve for x:

\left(2\right)^x=8

(a)

36.

Now let's solve for x:

5^x=25

(a)

37.

Let's practice some more.

2\left(3\right)^k=162

First we have to ____________

a)

isolate the exponential

b)

multiply 2 and 3

38.

First, isolate the exponential part by dividing both sides by 2

Then, find the value of k

2\left(3\right)^k=162

(a)

39.

How do we isolate the exponential part in this equation?

$\frac{1}{2}\left(7\right)^x=171.5$

a)

Divide both sides by 2

b)

Multiply both sides by 2

40.

When we multiply both sides by 2 we get $7^x=343$

What is the value of x?

(a)

41.

We get the same answer either way:

\left(3\right)^x=27

Now let's find the value of x

(a)

42.

Solve for t:

\frac{2}{5}\left(5\right)^t=250

(a)

43.

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

44.

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

45.

Evaluate log_b(b)

a)

-1

b)

0

c)

1

d)

b

46.

Evaluate log₉(9)

a)

-1

b)

1

c)

0

d)

9

47.

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

48.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

49.

Simplify log₄4^3x

a)

3x

b)

3

c)

4

d)

4^3x

50.

Condense

a)

A

b)

B

c)

C

d)

D

51.

Condense

a)

A

b)

B

c)

C

d)

D

52.

Condense

a)

A

b)

B

c)

C

d)

D

53.

Expand

a)

A

b)

B

c)

C

d)

D

54.

Expand

a)

A

b)

B

c)

C

d)

D

55.

a)

A

b)

B

c)

C

d)

D

56.

a)

A

b)

B

c)

C

d)

D

57.

Condense

a)

A

b)

B

c)

C

d)

D

58.

Expand log₆(5x³/y).

a)

log₆5x³-log₆y

b)

log₆5+log₆x³-log₆y

c)

log₆5+3log₆x-log₆y

59.

Rewrite log_b(xⁿ)

a)

nlog_bx

b)

(log_bx)ⁿ

c)

xⁿlog_bx

d)

log_b(xⁿ)

60.

a)

log₅(x²z²y¹⁰)

b)

log₅(z²y²x¹⁰)

c)

log(zy²x¹⁰)

d)

log₅(z² + y²+ x¹⁰)

61.

a)

6log₈(xyz)

b)

log₈(x) - log₈(y) - 6log₈(z)

c)

log₈(x) + log₈(y) - log₈(z)

d)

log₈(x) + log₈(y) + 6log₈(z)

62.

a)

log (a⁵+ b²⁵)

b)

log (a⁵− b²⁵)

c)

log (ab²⁵)

d)

log (a⁵/b²⁵)

63.

a)

log(x) + log(z) + 4log(y)

b)

3log(x) − log(z) − 4log(y)

c)

3log(x) + log(z) + 4log(y)

d)

log(x) − 4log(z) − 3log(y)

64.

Expand

a)

6log₈v-2log₈u

b)

6log₈u-2log₈v

c)

3log₈u-2log₈v

d)

6log₈u+2log₈v

65.

Which graph matches the function

*remember the transformation has shifted it right 3 and down 3

a)

b)

c)

d)

66.

Which graph matches the logarithmic equation

a)

b)

c)

d)

67.

Which graph is logarithmic

a)

b)

c)

d)

68.

Determine the range for the function

f(x) = 3(2)^x-4+ 5

a)

(4,∞)

b)

(2,∞)

c)

(3,∞)

d)

(5,∞)

69.

Find the domain.

a)

(-∞, 1)

b)

(-∞, ∞)

c)

(-∞, 0)

d)

(1,-∞)

70.

Describe the range of the function

a)

(-∞, 0)

b)

(0,∞)

c)

(-∞, ∞)

d)

(-3,∞)

e)

(-∞, 3)

71.

What is the transformation?

a)

Left 5

b)

Right 5

c)

Up 5

d)

Down 5

72.

What is the transformation?

a)

Left 5

b)

Right 5

c)

Up 5

d)

Down 5

73.

Describe the range of the exponential function shown

a)

$\left(-8,\infty\right)$

b)

$\left(-\infty,-8\right)$

c)

$\left(-\infty,\infty\right)$

d)

$\left(-8,0\right)$

74.

What is the domain of the function
y = -6^{x + 3} - 9

a)

(-∞, ∞)

b)

(-∞, -9)

c)

(-9, ∞)

d)

(∞, -∞)

75.

Describe the domain of the exponential function shown

a)

b)

c)

d)

76.

An initial investment of $1000 is deposited in an account with a 1.2% interest rate, compounded quarterly. Find the value after 15 years.

a)

$1045.96

b)

$1196.89

c)

$15180.81

d)

$5891.60

77.

Semi-Annually means how many times a year?

a)

4

b)

2

c)

1

d)

6

78.

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

79.

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

80.

Principal: $5000
Interest Rate: 3.75%
Time: 25 years
Compounded Monthly
State the future account balance.

a)

$12712.31

b)

$12,749.30

c)

$12,657.59

d)

$12550.84

81.

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%

82.

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

83.

The Arnold's took out a loan for $195,000 to purchase a home. At 4.3% interest rate compounded annually, how much will they have paid after 30 years?

a)

$412,749.79

b)

$529.305.61

c)

$689,546.99

d)

$640,891.53

84.

Shawn is buying a new Jet Ski for $12,500. He is considering 2 credit options. Option A offers a 6 year loan with 8.5% interest compounded quarterly, while Option B offers a 5 year loan with10% interest compounded annually.Which option is better and how much will he save?

a)

A) A; $495.21 raise money for charity

b)

B) A; $573.83 get attention

c)

C) B; $495.21 get on the news

d)

D) B; $573.83 do something crazy

85.

You want to save $5,000 for future family vacation. If the bank pays 4.3% compounded monthly for 3 years, then how much will you need to invest to reach your vacation goal?

a)

$307,042,791

b)

$5,000

c)

$3,250

d)

$4,395.89

86.

Jimmy invested $200 in a retirement account that had a rate of 20% that compounds annually. If Jimmy leaves his money puts the money in when he is 24 and takes it out when he is 64, how much money will be in his account rounded to the nearest dollar?

a)

$29395

b)

$293954.31

c)

$293954

87.

Matt wants to have a total of $3000 at the end of 5 years. if invested at 4.8% interest compounded semiannually how much should he put in the account in order to have $3000 at the end of the 5 years?

a)

$2473.04

b)

$2366.58

c)

$2067.95

d)

$1902.18

Exponential and Logarithm Test Review

Total questions: 87

Worksheet time: 5hrs 32mins

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