Free Printable Practice Quiz: Logarithms

1.

Write as one logarithm. Simplify, if possible.
log₂800 - log₂100

a)

8

b)

3

c)

-3

d)

1

2.

Write as one logarithm. Simplify, if possible.
log₅125 - log₅25

a)

1

b)

0

c)

5

d)

-1

3.

Write as one logarithm. Simplify, if possible.
log₆3 + log₆2

a)

0

b)

log₆5

c)

log₆1

d)

1

4.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

5.

Evaluate.
log₆(¹/₂₁₆)

a)

3

b)

¹/₃

c)

-¹/₃

d)

-3

6.

Write in logarithmic form.
5² = 25

a)

log₅2 = 25

b)

log₂25 = 5

c)

log₂₅5 = 2

d)

log₅25 = 2

7.

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

8.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

9.

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

10.

Expand

a)

log₈x + log₈y + log₈z

b)

5log₈x + 5log₈y + 5log₈z

c)

log₈xy + 5log₈z

d)

log₈x + log₈y + 5log₈z

11.

Write as a single logarithm:

log(30)-log(6)

a)

-6log(30)

b)

log(24)

c)

log(-24)

d)

log(5)

12.

Solve the equation for x.

a)

32

b)

25

c)

1.66

d)

512

13.

Solve for x:
log_x25 = 2

a)

5

b)

-5

c)

1/5

d)

-1/5

14.

Solve for x.
3^x = 27

a)

2

b)

4

c)

3

d)

5

15.

State the property (s) used to simplify the expression

log₄20 - 3log₄x = log₄(20/x³)

a)

Power Property

b)

Quotient Property

c)

Quotient and Power Property

d)

Product and Power Property

16.

Write the logarithm expression as a single logarithm

log₅4 + log₅3

a)

log₅7

b)

log₅12

c)

log₇5

d)

3log₅4

17.

Write the logarithm expression as a single logarithm

log₄60 - log₄4 + log₄x

a)

log₄15

b)

log₄15x

c)

log₄56x

d)

xlog₄30

18.

Write the logarithm expression as a single logarithm

2log 4 + log 2

a)

log 8

b)

log 16

c)

log 32

d)

log 8²

19.

Expand the logarithm expression

log 6x³y

a)

log 6x³ + log y

b)

log 6 + log x³ + log y

c)

3 log 6 + log x + log y

d)

log 6 + 3log x + log y

20.

log₄1 =

a)

0

b)

1

c)

4

d)

DNE

21.

Solve for x
log₈(x) = 2

a)

x = 256

b)

x = 64

c)

x = 16

d)

x = 32

22.

Solve for x:

a)

1

b)

2

c)

.5

d)

4

23.

log₁₆(4) = y

a)

y = 2

b)

y = 4

c)

y = (1/2)

d)

y = (1/4)

24.

log₂(1/8) = y

a)

y = -3

b)

y = (1/3)

c)

y = 3

d)

y = 0

25.

log₃(4x) = 2

a)

x=4/9
x=4/9

b)

x=9/4

c)

x=3/2

d)

x=2/3

26.

log₂(x + 5) = 3

a)

3

b)

4

c)

5

d)

6

27.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

28.

9^-1/2 = ?

a)

1/3

b)

-1/3

c)

1

d)

3

29.

log₈(4x+4)=2

a)

15

b)

12

c)

10

d)

3

30.

Solve for x:
2^{3x + 1} = 32

a)

0

b)

-1

c)

5/3

d)

4/3

31.

Solve the equation.

a)

2

b)

4

c)

11

d)

236

32.

Solve the equation.

a)

0

b)

-1

c)

1

d)

2

33.

Solve the equation.

a)

2/7

b)

3/7

c)

9/7

d)

13/7

34.

$2^{13x}=8$ Evaluate:

a)

8192

b)

3

c)

$\frac{3}{13}$

d)

256

35.

Solve for x.
$-6\log_{12}\left(x-5\right)=-6$

a)

-1

b)

-864

c)

2

d)

17

36.

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

a)

500

b)

100

c)

250

d)

5

37.

True or False? log(a − b) = log a − log b

a)

False

b)

True

38.

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)

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

39.

Expand the logarithm.
$\log_9\left(\frac{4^3}{5}\right)$

a)

$3\log_9\left(4\right)-3\log_9\left(5\right)$

b)

$3\log_9\left(4\right)-\log_9\left(5\right)$

c)

$\log_3\left(4\right)-\log_9\left(5\right)$

d)

$3\log_9\left(4\right)+\log_9\left(5\right)$

40.

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

41.

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

a)

5

b)

-2

c)

-5

d)

2

42.

log₂(x + 2) + log₂x = 3

a)

-4, 2

b)

-2, 4

c)

2

d)

1

43.

To solve, 16^5x = 64^x+7, what would be the correct set-up?

There is more than one correct answer.

a)

4^4(5x)= 4^16(x+7)

b)

8^2(5x)= 8^8(x+7)

c)

4^2(5x)= 4^3(x+7)

d)

2^4(5x)= 2^6(x+7)

44.

What is the domain of log(x)?

a)

(-∞, ∞)

b)

[0, ∞)

c)

(0, ∞)

d)

Pickle

45.

What are the transformations of this graph?

a)

Right 1 Up 5

b)

Right 1 Down 5

c)

Left 1 Up 5

d)

Left 1 Down 5

46.

Where is the asymptote?

a)

x = 1

b)

y = 1

c)

x = -1

d)

y = -1

47.

Describe the transformations of f(x)= -log₂(x+1)

a)

left 1

b)

left one & over the y-axis

c)

left one & over the x-axis

d)

right one & over the x axis

48.

What is the vertical asymptote of the equation $y=\log_5\left(x+3\right)+5$

a)

x = -3

b)

y = -3

c)

x = 5

d)

y = 5

49.

What is the range of the graph $y=\log_2\left(x-1\right)+3$

a)

(-∞, ∞)

b)

[-∞, ∞]

c)

[0, ∞)

d)

(0, ∞)

50.

What is the domain of the graph $y=\log_2\left(x-1\right)+3$

a)

(-1, ∞)

b)

[-1, ∞]

c)

[1, ∞)

d)

(1, ∞)

51.

Determine the order of transformations

a)

left 1, reflected over x-axis

b)

up 1, reflected over y-axis

c)

right 1, reflected over x-axis

d)

left 1, reflected over y-axis

52.

What is the range of log(x)?

a)

(-2, 4)

b)

(-∞, ∞)

c)

(-∞, 0)

d)

Cucumber

53.

As x --> 1, f(x) --> ____

a)

0

b)

∞

c)

-∞

d)

1

54.

As x --> ∞, f(x) --> ____

a)

0

b)

∞

c)

-∞

d)

1

55.

What is the domain?

a)

(-∞, ∞)

b)

(0, ∞)

c)

[1, ∞)

d)

(1, ∞)

Practice Quiz: Logarithms

Total questions: 55

Worksheet time: 9hrs 10mins

Similar Resources on Wayground