Free Printable Exponential and Logarithmic Review

1.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

2.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

3.

log₅25 = ?

a)

2

b)

5

c)

125

4.

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

5.

Condense: log₂6+log₂3=

a)

log₂18

b)

log₂2 = 1

c)

log₂3

d)

log₂9

6.

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

a)

log (12 + 2x)

b)

log (14x)

c)

log (12 * 2x)

d)

log (12x²)

7.

$\log\ 25\ +\ \log2\ =\ \log\ 27\$ True or False?

a)

True

b)

False

8.

Solve for x.
3^x = 27

a)

2

b)

4

c)

3

d)

5

9.

Evaluate the following logarithm:

log₃27

a)

3

b)

2

c)

-3

d)

¹/₃

10.

Evaluate the following logarithm:

log₅5

a)

1

b)

0

c)

-1

d)

¹/₂

11.

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

12.

Solve $\ln\left(3x-5\right)=6$

a)

136.143

b)

129.674

c)

150.578

d)

146.134

13.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

14.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

15.

$\left(\frac{1}{4}\right)^x=16^{^{ }2x+5}$

a)

4

b)

-5

c)

-2

d)

3

16.

log₂(x+3)=4

a)

16

b)

13

c)

3

d)

10

17.

$\log_6\left(x+5\right)+\log_6\left(4\right)=2$
Solve for x. Enter only numbers in your answer.

(a)

18.

Ms. Jones isn't sure if she solved this logarithmic equation correctly. Check her work to determine if she made any mistakes. If she did make a mistake, determine what it was.

a)

She did not convert to exponential form correctly.

b)

She did not distribute the 4 when combining the logs.

c)

She should have subtracted 2 from both sides instead of adding 2.

d)

No mistakes were made!

19.

Mrs. Cruise isn't sure if she solved this logarithmic equation correctly. Check her work to determine if she made any mistakes. If she did make a mistake, determine what it was.

a)

She did not convert to exponential form correctly.

b)

She should have divided the arguments.

c)

She used the incorrect base when converting to exponential form.

d)

No mistakes were made!

20.

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)

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

21.

Condense: $\frac{1}{2}\log_3x\ +\ 5\log_3y$

a)

$\log_3\left(\sqrt{xy^5\ }\right)$

b)

$\log_3\left(\sqrt{x}\ y^5\right)$

c)

$\log_3\left(5\sqrt{x}y\right)$

d)

$\log_3\left(xy\right)^{\frac{5}{2}}$

22.

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)

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

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.

Rewrite in logarithmic form.

8^m-7 = 92

a)

8⁹² = m - 7

b)

92 = 8(m - 7)

c)

log₈92 = m - 7

d)

log_(m-7)92 = 8

25.

Solving Log Equations: Use Properties of logarithms to solve the given equation for the variable and choose the correct solution.

a)

A

b)

B

c)

C

d)

D

26.

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

a)

5

b)

-5

c)

1/5

d)

-1/5

27.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

28.

Condense: log₂6+log₂3=

a)

log₂18

b)

log₂2 = 1

c)

log₂3

d)

log₂9

29.

Expand/Write as multiple logs.

log (2x³)

a)

log 2 + 3 log x

b)

3 log 2x

c)

log 2* 3 log x

d)

2 log x³

30.

Solve for x.
5^x = 1

a)

0

b)

-1

c)

2

d)

1

31.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

32.

Rewrite as two logarithms.

a)

A

b)

B

c)

C

d)

D

33.

The natural logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

34.

Evaluate:
$\ln3=x$

a)

$0.405$

b)

$1.099$

c)

$1.504$

d)

$1.792$

35.

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

36.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

37.

Rewrite log₂8 = 3 in exponential form

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

38.

Solve for x:
log_x25 = 2

a)

5

b)

-5

c)

1/5

d)

-1/5

39.

Evaluate log₄1

a)

1

b)

0

c)

4

d)

undefined

40.

Write the logarithm expression as a single logarithm

log₆25 - log₆5

a)

log₆125

b)

log₅20

c)

log₆5

d)

log₆30

41.

Write the logarithm expression as a single logarithm

2log 4 + log 2

a)

log 8

b)

log 16

c)

log 32

d)

log 8²

42.

Expand the logarithm.

a)

A

b)

B

c)

C

d)

D

43.

Solve the equation.

a)

A

b)

B

c)

C

d)

D

44.

Expand

a)

6log₈v-2log₈u

b)

6log₈u-2log₈v

c)

3log₈u-2log₈v

d)

6log₈u+2log₈v

45.

Expand.

a)

1/3 log x + log y + log z

b)

1/3 log x + 1/3 log y + 1/3 log z

c)

1/3 log x - 1/3 log y - 1/3 log z

d)

3 log x + 3 log y + 3 log z

46.

Expand log₆(5x³/y).

a)

log₆5x³-log₆y

b)

log₆5+log₆x³-log₆y

c)

log₆5+3log₆x-log₆y

47.

Condense

a)

A

b)

B

c)

C

d)

D

48.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

49.

log(4x)

a)

log4-logx

b)

log4+logx

c)

4logx

d)

xlog4

50.

log(x⁷)

a)

log(7x)

b)

log7+logx

c)

xlog7

d)

7logx

51.

Rewrite as a single logarithm:

\log_260\ -\ \log_210

a)

$\log_26$

b)

$\log_250$

c)

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

d)

$\log_270$

52.

Rewrite each equation in logarithmic form.

a)

A

b)

B

c)

C

d)

D

53.

Rewrite log_vn = a in exponential form.

a)

v^a = n

b)

n^a = v

c)

vⁿ = a

d)

aⁿ = v

54.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

55.

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

56.

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

57.

Evaluate the logarithm. Type in the number only for the answer.

$\log_{18}1$

(a)

58.

Condense the Logarithm: $\log_4x+\log_4y$

a)

$4\log xy$

b)

$\log_4xy$

c)

$y\log_4x$

d)

$\log_4\ \frac{x}{y}$

59.

Condense into a single logarithm.

a)

A

b)

B

c)

C

d)

D

60.

Evaluate the logarithm. Type in the number only for the answer.

$\log_7\ \frac{1}{7}$

(a)

61.

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)

$\log_65+3\log_6x+\log_6y$

62.

Condense into a single logarithm.

a)

A

b)

B

c)

C

d)

D

63.

Condense. (Be careful with the order of the answer choices, they are at random.)

a)

A

b)

B

c)

C

d)

D

64.

Rewrite in exponential form.

a)

A

b)

B

c)

C

d)

D

65.

Evaluate the logarithm. Type in the number only for the answer.

$\log_{100}10$

(a)

66.

Expand

a)

log₈x + log₈y + log₈z

b)

5log₈x + 5log₈y + 5log₈z

c)

log₈xy + 5log₈z

d)

log₈x + log₈y + 5log₈z

67.

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)

$\log x-\log6y$

68.

Expand the logarithm.

a)

A

b)

B

c)

C

d)

D

69.

log₈(4x+4)=2

a)

15

b)

12

c)

10

d)

3

70.

$\log_{\left(x-1\right)}\left(6x-14\right)=2$ Solve for all values of x:

a)

x=6 and x=4

b)

x=5 and x=3

c)

x=1 and x=-3

d)

x=2 and x=5

71.

Solve for x:
log₄ x = 3

a)

4

b)

12

c)

32

d)

64

72.

Solve for x:

log₈(4x+4)=2

a)

15

b)

12

c)

10

d)

3

73.

Solve for x:

log_x1000=3

a)

1

b)

10

c)

30

d)

3

74.

Solve for x:
log₄ x = 3

a)

4

b)

12

c)

32

d)

64

75.

Solve for x:

log(x+6) = 1

a)

4

b)

4.222

c)

-5

d)

-9.550

76.

How would you solve an exponential equation like the one below:
$4^{2x-3}=4^{6x+5}$

a)

Rewrite $4$ as $2^2$

b)

Multiply the exponents

c)

Set the exponents equal to each other

d)

Add the exponents

77.

Solve 3²⁶ = 3^{4x + 2}

a)

x = 6

b)

x = 5

c)

x = 3

d)

x = -4

78.

Solve 7^3x+2 = 7^{x - 8}

a)

-5

b)

-4

c)

2

d)

-3

79.

Solve for x using the same base method.
3^x-20= 27

a)

17

b)

27

c)

-7

d)

23

80.

2^x+6=32

a)

x=-1

b)

x=11

c)

x=1

d)

x=-11

81.

log₂(x + 5) = 3

a)

3

b)

4

c)

5

d)

6

82.

4^(x-2)= 64^(x+1)

a)

-2/5

b)

-5/2

c)

7/2

d)

2/7

83.

Solve

a)

1

b)

0

c)

-1

d)

Undefined

84.

Solve

a)

1/3

b)

-1/3

c)

-3

d)

3

85.

Solve:

log₃(x - 5) = 2

a)

25

b)

5

c)

130

d)

14

86.

log₆(2x + 3) = 3

a)

x = 106.5

b)

x = 100

c)

x = 16

d)

x = 50

87.

Solve

a)

1

b)

-1

c)

6

d)

-6

88.

Solve

a)

-1/4

b)

1/4

c)

4

d)

-4

Exponential and Logarithmic Review

Total questions: 88

Worksheet time: 8hrs 11mins

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