Free Printable Practice with Logs

1.

Rewrite in exponential form $\frac{1}{2}=\log_{25}5$

a)

$25^{\frac{1}{2}}=\ 5$

b)

$5^2\ =\ \ 25$

c)

50/2 = 25

d)

100/4 = 25

2.

Rewrite log_x95 = 2.3

a)

x^2.3 = 95

b)

95^2.3 = x

c)

2.3⁹⁵ = x

d)

x⁹⁵= 2.3

3.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

4.

log₃81 =

a)

2

b)

3

c)

4

d)

5

5.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

6.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

7.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

8.

log₅25 = ?

a)

2

b)

5

c)

125

9.

Write the exponential equation as a logarithm
6³=216

a)

log₆(3) = 216

b)

log₃(6) = 216

c)

log₆(216)=3

d)

log₂₁₆(6)=3

10.

The following:
log₂ 16 = 4 can be written as...

a)

2¹⁶=4

b)

4²=16

c)

4+4+4+4=16

d)

2⁴=16

11.

Change to Logarithmic Form:
12² = 144

a)

log₂ 144 = 12

b)

log₁₂ 144 = 2

c)

log ₁₂ 2 = 144

d)

log ₂ 12 = 144

12.

Rewrite log₂8 = 3 in exponential form.

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

13.

Change to Logarithmic Form:
5³ = 125

a)

log ₅ 125 = 3

b)

log₃125 = 5

c)

log ₅ 3 =125

d)

log₁₂₅ 3 = 5

14.

Change to Exponential Form:
log₂₈₉ 17 = 1/2

a)

289^1/2 = 17

b)

17^1/2 = 289

c)

289¹⁷ = 1/2

d)

1/2¹⁷ = 289

15.

Evaluate:
log₄16

a)

2

b)

4

c)

1/2

d)

-2

16.

Rewrite in logarithmic form. 9^3/2=27

a)

log₉27=3/2

b)

log₉27=2/3

c)

log_3/29=27

d)

log₂₇9=3/2

17.

Rewrite in logarithmic form. 7⁰=1

a)

log₀7=1

b)

log₇0=1

c)

log₇1=0

d)

log₁7=0

18.

Evaluate.
log₆(¹/36)

a)

2

b)

¹/2

c)

-¹/2

d)

-2

19.

Evaluate:
log₄16

a)

2

b)

4

c)

1/2

d)

-2

20.

$Evaluate\ \log_864$

(a)

21.

$Evaluate\ \log_28$

(a)

22.

$Evaluate\ \log_93$

(a)

23.

$Evaluate\ \log_7\frac{1}{49}$

(a)

24.

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)

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

25.

Write in exponential form: $\log_2128=7$

a)

$2^7=128$

b)

$7^2=128$

c)

$2^{128}=7$

d)

$7^{128}=2$

26.

Write in exponential form: $\log_3\frac{1}{27}=-3$

a)

$3^{-3}=\frac{1}{27}$

b)

$-3^3=\frac{1}{27}$

c)

$\left(\frac{1}{27}\right)^{-3}=3$

d)

$3^{\frac{1}{27}}=-3$

27.

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

a)

$\log_4256=4$

b)

$\log_{256}4=4$

c)

$\log_4256=256$

d)

$\log_44=256$

28.

Write in logarithmic form: $8^3=512$

a)

$\log_8512=3$

b)

$\log_3512=8$

c)

$\log_83=512$

d)

$\log_{256}8=3$

29.

Evaluate $\log_636$

a)

2

b)

3

c)

4

d)

6

30.

Evaluate: $\log_232$

a)

6

b)

5

c)

2

d)

3

31.

Evaluate: $\log_381$

a)

9

b)

2

c)

3

d)

4

32.

$\log_{18}1$

a)

0

b)

1

c)

2

d)

18

33.

$\log\ 1000$

a)

3

b)

2

c)

10

d)

1

34.

Evaluate: $\log_2\frac{1}{16}$

a)

-4

b)

1/4

c)

-3

d)

-8

35.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

36.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

37.

Evaluate the following logarithm:

log₅5

a)

1

b)

0

c)

-1

d)

¹/₂

38.

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

39.

Write in logarithmic form.
5² = 25

a)

log₅2 = 25

b)

log₂25 = 5

c)

log₂₅5 = 2

d)

log₅25 = 2

40.

Evaluate:
log₄16

a)

2

b)

4

c)

1/2

d)

-2

41.

Change y = a^xinto log form.

a)

x = log_ay

b)

y = log_ax

c)

x = log_ya

d)

y = log a

42.

Solve for x:

a)

6

b)

18

c)

72

d)

No solution

43.

Evaluate:

a)

1

b)

2

c)

$\frac{1}{2}$

d)

4

44.

a)

A

b)

B

c)

C

d)

D

45.

a)

A

b)

B

c)

C

d)

D

46.

a)

A

b)

B

c)

C

d)

D

47.

a)

A

b)

B

c)

C

d)

D

48.

a)

A

b)

B

c)

C

d)

D

49.

a)

A

b)

B

c)

C

d)

D

50.

a)

A

b)

B

c)

C

d)

D

51.

a)

A

b)

B

c)

C

d)

D

52.

a)

A

b)

B

c)

C

d)

D

53.

ln (5x + 6) = 5

a)

154.413

b)

30.883

c)

147.213

d)

28.483

54.

Rewrite e^x = 9 using a logarithm

a)

ln x = 9

b)

ln 9 = x

c)

log_x e = 9

d)

log₉ x = e

55.

What is the value of ln(e⁷)

a)

2.718...

b)

1

c)

7

d)

Does not exist

56.

Rewrite in exponential form:
ln(2) = x

a)

2^x= 10

b)

10² = x

c)

e^x= 2

d)

e² = x

57.

Which of the following is the value of x given;
e^(x+6) = 12

a)

x = ln 6

b)

x = -6 + ln12

c)

x = ln72

d)

x = ln(-2)

58.

ln e⁵=

a)

e⁵

b)

ln 5

c)

5

d)

5e

59.

Solve for x:

ln(x)=2

a)

2.234

b)

3.14

c)

7.389

d)

2

60.

If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

a)

$1,225,54

b)

$2,225.54

c)

$22,255.40

d)

$225.54

Practice with Logs

Total questions: 60

Worksheet time: 2hrs 15mins

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