Free Printable Exponential & Logarithmic Functions Test

1.

Choose the equation that correctly displays the exponential equation $7^x=\tfrac{1}{49}$ in logarithmic form.

a)

$\log_x \tfrac{1}{49}=7$

b)

$\log_7 x=\tfrac{1}{49}$

c)

$\log_7 \tfrac{1}{49}=x$

d)

$\log_x 7=\tfrac{1}{49}$

2.

Choose the equation that correctly displays the logarithmic equation $\log_3 x=4$ in exponential form.

a)

$3^4=x$

b)

$4^3=x$

c)

$3^x=4$

d)

$4^x=3$

3.

Choose the equation that correctly displays the exponential equation $e^x=5.43$ in logarithmic form.

a)

$\log_x 5.43=e$

b)

$\ln 5.43=x$

c)

$\log_{5.43} e=x$

d)

$\ln x=5.43$

4.

Solve the basic log equation for the value of the variable: $\log_4 64=x$ .

a)

$x=3$

b)

$x=4$

c)

$x=16$

d)

$x=32$

5.

Choose the answer choice that correctly expands the logarithm: $\log_5 a^2 b^3$ .

a)

$2\log_5 a-3\log_5 b$

b)

$\log_5 a^2-\log_5 b^3$

c)

$2\log_5 a+3\log_5 b$

d)

$\log_5 a^2+\log_5 b^3$

6.

Solve the exponential equation: $2^{x-4}=8^{x+2}$ . Round your answer to the thousandths place, when necessary.

a)

$x=-5$

b)

$x=5$

c)

$x=2$

d)

$x=-2$

7.

Solve the exponential equation: $\left(\tfrac{1}{9}\right)^{2x}=(27)^{-x+2}$ . Round your answer to the thousandths place, when necessary.

a)

$x=-6$

b)

$x=6$

c)

$x=-2$

d)

$x=2$

8.

Solve the exponential equation: $6^{x-4}=17$ . Round your answer to the thousandths place, when necessary.

a)

$x=5.582$

b)

$x=5.167$

c)

$x=6.000$

d)

$x=4.263$

9.

Solve the exponential equation: $4^{2x-1}=25$ . Round your answer to the thousandths place, when necessary.

a)

$x=1.000$

b)

$x=1.661$

c)

$x=2.322$

d)

$x=3.000$

10.

Solve the logarithmic equation: $\log_5(3x-8)=2$ . Round your answer to the thousandths place, when necessary.

a)

$x=11$

b)

$x=8$

c)

$x=25$

d)

$x=33$

11.

Solve the logarithmic equation: $\log_4\left(\tfrac{2x}{3}\right)=2$ . Round your answer to the thousandths place, when necessary.

a)

$x=12$

b)

$x=24$

c)

$x=32$

d)

$x=48$

12.

Solve the logarithmic equation: $\log_3 x+\log_3(x+6)=\log_3 16$ . Round your answer to the thousandths place, when necessary.

a)

$x=2$

b)

$x=8$

c)

$x=16$

d)

$x=-8$

13.

Solve the basic log equation for the value of the variable. $\log_4 x = 2$

a)

$x=3$

b)

$x=4$

c)

$x=16$

d)

$x=32$

14.

Choose the answer choice that correctly expands the following logarithm: $\log_5\!\left(a^2 b^3\right)$

a)

$2\log_5 a + 3\log_5 b$

b)

$\log_5 a^2 + \log_5 b^3$

c)

$2\log_5 a - 3\log_5 b$

d)

$\log_5 a^2 - \log_5 b^3$

15.

Choose the answer choice that correctly condenses the following logarithm: $4\ln x + \tfrac{1}{2}\ln y - 2\ln 3 - 6\ln z$

a)

$\ln\!\left(9x^4 y^{1/2} z^6\right)$

b)

$\ln\!\left(\tfrac{x^4 y^{1/2}}{9 z^6}\right)$

c)

$\ln\!\left(\tfrac{4xy}{6z}\right)$

d)

$\ln\!\left(\tfrac{3z^6}{x^4 y^2}\right)$

16.

Free Response. For problems 14–20, solve the exponential or logarithmic equations for the value of the variable. Round all answers to the thousandths place, when necessary. Record your answer in the space provided. Solve the following exponential equation: $2^{x-4}=16^{x+2}$ .

a)

$x=-3$

b)

$x=-4$

c)

$x=4$

d)

$x=0$

17.

Free Response. For problems 14–20, solve the exponential or logarithmic equations for the value of the variable. Round all answers to the thousandths place, when necessary. Record your answer in the space provided. Solve the following exponential equation: $\left(\tfrac{1}{9}\right)^{6x}=(27)^{-x+3}$ .

a)

$x=1$

b)

$x=-1$

c)

$x=3$

d)

$x=-3$

18.

Free Response. For problems 14–20, solve the exponential or logarithmic equations for the value of the variable. Round all answers to the thousandths place, when necessary. Record your answer in the space provided. Solve the following exponential equation: $4^{2x-1}=25$ .

a)

$x=0.839$

b)

$x=1.661$

c)

$x=2.322$

d)

$x=1.500$

19.

Free Response. For problems 14–20, solve the exponential or logarithmic equations for the value of the variable. Round all answers to the thousandths place, when necessary. Record your answer in the space provided. Solve the following exponential equation: $6^{x-4}=17$ .

a)

$x=4.418$

b)

$x=5.582$

c)

$x=1.582$

d)

$x=6.000$

20.

Free Response. For problems 14–20, solve the exponential or logarithmic equations for the value of the variable. Round all answers to the thousandths place, when necessary. Record your answer in the space provided. Solve the following logarithmic equation: $\log_2 (3x-10)=3$ .

a)

$x=4$

b)

$x=6$

c)

$x=9$

d)

$x=2$

21.

Solve the following logarithmic equation: $\log_5\!\left(\tfrac{25x}{4}\right)=2$ .

a)

$x=0.16$

b)

$x=0.25$

c)

$x=4$

d)

$x=6$

22.

Solve the following logarithmic equation: $\log_3 x + \log_3 (x+6) = \log_3 16$ .

a)

$x=-8$

b)

$x=2$

c)

$x=4$

d)

$x=8$

23.

Expand

a)

6log₈v-2log₈u

b)

6log₈u-2log₈v

c)

3log₈u-2log₈v

d)

6log₈u+2log₈v

24.

Expand

a)

log₈x+log₈y+log₈z

b)

5log₈x+5log₈y+5log₈z

c)

log₈xy+5log₈z

d)

log₈x+log₈y+5log₈z

25.

Expand

a)

5log₅a - 6log₅b

b)

5log₅a - 30log₅b

c)

5log₅a + 30log₅b

d)

30log₅b - 5log₅a

26.

Expand

a)

A

b)

B

c)

C

d)

D

27.

Expand

a)

A

b)

B

c)

C

d)

D

28.

Expand.

a)

A

b)

B

c)

C

d)

D

29.

Condense.

a)

A

b)

B

c)

C

d)

D

30.

Condense.

a)

A

b)

B

c)

C

d)

D

31.

Condense.

a)

A

b)

B

c)

C

d)

D

32.

Condense.

a)

A

b)

B

c)

C

d)

D

33.

Condense.

a)

A

b)

B

c)

C

d)

D

34.

Write the expression as a single logarithm. Then simplify if possible.

log₅3 + log₅6 + log₅9

a)

log₅69

b)

log₅56

c)

log₅162

d)

log₅98

35.

Expand

\log_5\left(\frac{19}{2}\right)

a)

$\log_219-\log_25$

b)

$\log_{19}2-\log_52$

c)

$\log_519-\log_52$

d)

$\log_52-\log_519$

36.

Expand

\log_26a

a)

$\log_26+\log_2a$

b)

$\log_a6+\log_a2$

c)

$\log_6a+\log_2a$

d)

$\log_62+\log_6a$

37.

Expand

\log_2\left(9^5\right)

a)

$9\log_25$

b)

$5\log_29$

c)

$2\log_59$

d)

$5\log_92$

38.

Expand

\log_5\left(\frac{12a}{2}\right)

a)

$\log_212a-\log_25$

b)

$\log_512a-\log_52$

c)

$\log_512-\log_5a-\log_52$

d)

$\log_512+\log_5a-\log_52$

39.

Condense

\log3+\log x

a)

$\log\left(3x\right)$

b)

$\log\left(3^x\right)$

c)

$\log\left(3+x\right)$

d)

$\log_35$

40.

Condense

\log5-\log4

a)

$\log\left(5-4\right)$

b)

$\log\left(\frac{4}{5}\right)$

c)

$\log\left(\frac{5}{4}\right)$

d)

$\log\left(5^{-4}\right)$

41.

Condense

$2\log_8x$

a)

$\log_82x$

b)

$8\log_2x$

c)

$\log_28x$

d)

$\log_8x^2$

42.

Condense

\log_3x+2\log_3y

a)

$\log_3\left(x+2y\right)$

b)

$\log_3\left(xy^2\right)$

c)

$\log_3\left(x\cdot2y\right)$

d)

$2\log_3xy$

43.

Condense and Simplify

\log_33+\log_327

a)

$\log_330\ =\ 10$

b)

$\log_381=4$

c)

$\log_39=2$

d)

$\log_324=8$

44.

Condense

a)

A

b)

B

c)

C

d)

D

45.

Condense

a)

A

b)

B

c)

C

d)

D

46.

CONDENSE

a)

A

b)

B

c)

C

d)

D

47.

Condense

a)

A

b)

B

c)

C

d)

D

48.

Condense

a)

A

b)

B

c)

C

d)

D

49.

Condense

a)

A

b)

B

c)

C

d)

D

50.

Expand

a)

A

b)

B

c)

C

d)

D

51.

Expand

a)

A

b)

B

c)

C

d)

D

52.

Expand

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.

Expand

a)

A

b)

B

c)

C

d)

D

56.

Expand

a)

A

b)

B

c)

C

d)

D

57.

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

a)

5

b)

-2

c)

-5

d)

2

58.

log₂(x + 2) + log₂x = 3

a)

-4, 2

b)

-2, 4

c)

2

d)

1

59.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

60.

Solve

a)

A

b)

B

c)

C

d)

D

61.

a)

5

b)

13

c)

84

d)

-20

62.

a)

no solution

b)

only 6

c)

6 and -2

d)

3

63.

log₄(3x-1)=log₄(2x+3)

a)

4

b)

3

c)

1

d)

8

64.

log₂(x²- 6) = log₂(2x+2)

a)

4, -2

b)

No Solution

c)

4

d)

-2

65.

log₂(x+3)=4

a)

16

b)

13

c)

3

d)

10

66.

log_x1000=3

a)

1

b)

10

c)

30

d)

3

67.

log₈(4x+4)=2

a)

15

b)

12

c)

10

d)

3

68.

a)

x is undefined

b)

x = 2

c)

x= 0.4

d)

x = 33

69.

a)

x = 5 and x = -2

b)

x = -2

c)

x = 5

d)

x = -10 and x = 10

70.

a)

x = 21

b)

x= 49/3

c)

x = 49

d)

x = 147

71.

Solve

a)

1

b)

-1

c)

6

d)

-6

72.

Solve

a)

A

b)

B

c)

C

d)

D

73.

Q1. What is the result of 5 + 3?

a)

A) 150

b)

B) -18

c)

C) 85

d)

D) 11

74.

Solve

a)

-3

b)

3

c)

1/3

d)

-1/3

75.

a)

5

b)

13

c)

84

d)

-20

76.

Solve for x:

a)

10001

b)

999

c)

No Solution

d)

3^-12+

77.

Solve

a)

8

b)

-8

c)

1/8

d)

-1/8

78.

log₉(10)-log₉(x-3) =log₉(72)

a)

81/16

b)

113/36

c)

No Solution

d)

92/15

79.

log₉(x)+log₉(x+2)=log₉(35)

a)

5

b)

-7

c)

5, -7

d)

-7, -13

80.

log₅x - log₅(x+4)=log₅38

a)

-152/37, -8

b)

1/2

c)

-152/37

d)

No Solution

81.

log7+log(x²-4)=log35

a)

-1

b)

-2

c)

-3

d)

-4

82.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

83.

log₄(3x-1)=log₄(2x+3)

a)

4

b)

3

c)

1

d)

8

84.

log₈(6-5x) = log₈(3- 4x)

a)

3

b)

No Solution

c)

9

d)

1

Exponential & Logarithmic Functions Test

Total questions: 84

Worksheet time: 4hrs 8mins

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