Free Printable Exponential and Logarithmic Form Problems

1.

Write in logarithmic form.
5² = 25

a)

log₅2 = 25

b)

log₂25 = 5

c)

log₂₅5 = 2

d)

log₅25 = 2

2.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

3.

Write in logarithmic form.
5² = 25

a)

log₅2 = 25

b)

log₂25 = 5

c)

log₂₅5 = 2

d)

log₅25 = 2

4.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

5.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

6.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

7.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

8.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

9.

Evaluate Logarithms: Find the value of the given logarithm.

$\log_232=$

a)

2

b)

3

c)

4

d)

5

10.

Converting forms: Convert the given exponential equation into its logarithmic form.

$3^x=y$

a)

$\log_3x=y$

b)

$\log_3y=x$

c)

$\log_xy=3$

d)

$\log_yx=3$

11.

Converting forms: Convert the given logarithmic equation into its exponential form. $\log_x25=3$

a)

$x^3=25$

b)

$3^x=25$

c)

$25^3=x$

d)

$25^x=3$

12.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

13.

Rewrite as an exponential: log₂8 = 3

a)

3² = 8

b)

2³ = 8

c)

2⁸ = 3

d)

8³ = 2

14.

Rewrite as an exponential: $\log_7\left(\frac{1}{49}\right)=-2$

a)

$7^{\frac{1}{49}}=-2$

b)

$\left(\frac{1}{49}\right)^{-2}=7$

c)

$7^{-2}=\frac{1}{49}$

d)

$\left(-2\right)^7=\frac{1}{49}$

15.

Rewrite as an exponential: $\log_93=\frac{1}{2}$

a)

$9^{\frac{1}{2}}=3$

b)

$3^{\frac{1}{2}}=9$

c)

$9^3=\frac{1}{2}$

d)

$\left(\frac{1}{2}\right)^9=3$

16.

Rewrite as a log: y = 7^x

a)

log₇(x) = y

b)

log_y(7) = x

c)

log_x(y) = 7

d)

log₇(y) = x

17.

Write in logarithmic form: $4^4=256$

a)

$\log_4256=4$

b)

$\log_{256}4=4$

c)

$\log_4256=256$

d)

$\log_44=256$

18.

Write in exponential form:

log ₂ 32 = 5

a)

2⁵ = 32

b)

5² = 32

c)

5³² = 2

d)

2³² = 5

19.

Write in exponential form:
log ₃ 6561 = 8

a)

3⁸ = 6561

b)

8³ = 6561

c)

3⁶⁵⁶¹= 8

d)

8⁶⁵⁶¹ = 3

20.

Write in logarithmic form:
9² = 81

a)

log ₉ 81 = 2

b)

log ₂ 81 = 9

c)

log ₉ 2 = 81

d)

log ₂ 9 = 81

21.

Write in logarithmic form:
4⁵ = 1024

a)

log ₄ 1024 = 5

b)

log ₅ 1024 = 4

c)

log ₄ 5 = 1024

d)

log ₅ 4 = 1024

22.

Evaluate log₅25 = x

a)

2

b)

5

c)

125

23.

Rewrite the equation in logarithmic form.

a)

A

b)

B

c)

C

d)

D

24.

Rewrite in exponential form.

a)

A

b)

B

c)

C

d)

D

25.

Rewrite in exponential form.

a)

A

b)

B

c)

C

d)

D

26.

Convert between logarithmic and exponential form

[Click on the image if you need to make it larger]

a)

A

b)

B

c)

C

d)

D

27.

Convert between logarithmic and exponential form

[Click on the image if you need to make it larger]

a)

A

b)

B

c)

C

d)

D

28.

Convert between logarithmic and exponential form

[Click on the image if you need to make it larger]

a)

A

b)

B

c)

C

d)

D

29.

Convert to exponential form: $\log_2x=16$

a)

$2^x=16$

b)

$x^2=16$

c)

$16^2=x$

d)

$2^{16}=x$

30.

Rewrite: $11^x=121$

a)

$\log_{11}x=121$

b)

$\log_{121}x=11$

c)

$\log_{11}121=x$

d)

$\log_x11=121$

31.

Which of the following are examples of perfect squares?

a)

4

b)

6

c)

9

d)

25

32.

27 is a perfect cube

a)

true

b)

false

33.

The inverse operation for SQUARING a number is finding the CUBE root?

a)

true

b)

false

34.

$\sqrt{36}=$

a)

4

b)

9

c)

6

d)

12

35.

100 is a ____________

a)

Perfect Square

b)

Perfect Cube

c)

Both

d)

Neither

36.

$3\sqrt{64}=$

a)

8

b)

5

c)

4

d)

12

37.

Select all the PERFECT SQUARES

a)

10

b)

144

c)

9

d)

8

38.

Select all the PERFECT CUBES

a)

8

b)

2

c)

125

d)

27

39.

$x^2=100.\ \ What\ does\ x=?$

a)

0

b)

90

c)

1

d)

10

40.

Squaring a number means multiplying a number by itself.

a)

True

b)

False

41.

Cubing a number means multiplying a number by itself 3 times.

a)

True

b)

False

42.

$\sqrt[3]{125}$

a)

5

b)

-5

c)

62.5

d)

32

43.

$\sqrt[3]{8}$

a)

2

b)

-2

c)

-4

d)

16

44.

$x^2=64$

a)

8

b)

$\pm8$

c)

4

d)

$\pm4$

45.

$x^2=36$

a)

$\pm6$

b)

6

c)

-6

d)

12

46.

$x^3=27$

a)

$\pm3$

b)

13.5

c)

3

d)

-3

47.

$x^2=121$

a)

11

b)

-11

c)

$\pm11$

d)

$\pm13$

48.

Find the two square roots of the number; 16

a)

4, -4

b)

16, -16

c)

2, -2

d)

8, -8

49.

What does this symbol represent?

a)

square root

b)

divide by 2

c)

cube root

d)

greater than or less than

50.

$9^2=18$ True or false?

a)

True

b)

False

51.

$3_{\sqrt{8}}$ (cube root of 8)

a)

2

b)

$\pm2$

c)

-2

d)

None of the above

52.

Select the set with all perfect squares.

a)

-144, 9, 50, 75, 81, 100

b)

9, 50, 81, 100

c)

9, 50, 75, 81, 100

d)

9, 81, 100

Exponential and Logarithmic Form Problems

Total questions: 52

Worksheet time: 2hrs 7mins

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