Free Printable Logarithms

1.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

2.

Write in logarithmic form.
5² = 25

a)

log₅2 = 25

b)

log₂25 = 5

c)

log₂₅5 = 2

d)

log₅25 = 2

3.

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

4.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

5.

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

6.

Evaluate:
log₄16

a)

2

b)

4

c)

1/2

d)

-2

7.

Evaluate.
Log₂64

a)

A

b)

B

c)

C

d)

D

8.

log₄1 =

a)

0

b)

1

c)

4

d)

DNE

9.

Rewrite log₂8 = 3 in exponential form

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

10.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

11.

Evaluate the following logarithm:

log₃27

a)

3

b)

2

c)

-3

d)

¹/₃

12.

Evaluate the following logarithm:

log₄16

a)

1

b)

-2

c)

2

d)

¹/₂

13.

Evaluate the following logarithm:

log₅5

a)

1

b)

0

c)

-1

d)

¹/₂

14.

Evaluate.
log₆(¹/₂₁₆)

a)

3

b)

¹/₃

c)

-¹/₃

d)

-3

15.

Write as one logarithm. Simplify, if possible.
log₃9 + log₃27

a)

-1

b)

5

c)

4

d)

1

16.

Rewrite e^x = 9 using a logarithm

a)

ln x = 9

b)

ln 9 = x

c)

log_x e = 9

d)

log₉ x = e

17.

What is the log form of a = e^y ?

a)

ln(a) = y

b)

ln(y) = a

c)

log(a) = y

d)

log(y) = a

18.

Evaluate the log:
log₃(1/9) =

a)

1/2

b)

2

c)

-2

d)

3

19.

Evaluate log_b(b)

a)

-1

b)

0

c)

1

d)

b

20.

log₅25 = ?

a)

2

b)

5

c)

125

21.

log ₃9 =

a)

1/2

b)

2

c)

1/3

d)

3

22.

log ₁₆ 8 =

a)

1/2

b)

4/3

c)

2

d)

3/4

23.

log 1000 =

a)

1/10

b)

10

c)

1/3

d)

3

24.

log ₃₂ 4 =

a)

1/8

b)

8

c)

5/2

d)

2/5

25.

log ₁₇ 1

a)

1

b)

0

c)

17

d)

18

26.

Solve for x:
log₄ x = 3

a)

4

b)

12

c)

32

d)

64

27.

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

28.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

29.

Evaluate $\log_3\left(\ \frac{1}{3}\right)$

a)

10

b)

1

c)

0

d)

-1

30.

f(x)=log₅(x+4) - 2

Describe the asymptote

a)

Horizontal Asymptote x = -4

b)

Vertical Asymptote x = -4

c)

Horizontal Asymptote x = 4

d)

Vertical Asymptote x = 4

31.

What is the asymptote for the logarithmic function

$f\left(x\right)=\log\left(x-1\right)$

a)

x=1

b)

x=-1

c)

y=1

d)

y=-1

32.

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

a)

log (12 + 2x)

b)

log (14x)

c)

log (12 * 2x)

d)

log (12x²)

33.

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

34.

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

a)

True

b)

False

35.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

36.

Rewrite as two logarithms.

a)

A

b)

B

c)

C

d)

D

37.

Evaluate the logarithmic expression without a calculator:

\log_{15}15

a)

0

b)

15

c)

1

d)

-1

38.

The natural logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

39.

Write the logarithm expression as a single logarithm

log₆25 - log₆5

a)

log₆125

b)

log₅20

c)

log₆5

d)

log₆30

40.

Write the logarithm expression as a single logarithm

2log 4 + log 2

a)

log 8

b)

log 16

c)

log 32

d)

log 8²

41.

Expand

a)

6log₈v-2log₈u

b)

6log₈u-2log₈v

c)

3log₈u-2log₈v

d)

6log₈u+2log₈v

42.

What is the most simple answer possible:
log_x(x³y) - log_x(xy)

a)

log_x(x²)

b)

2

c)

log_x(x⁴-y²)

d)

x

43.

Logarithms are the inverse of ___________.

a)

Trees

b)

Quadratics

c)

Square

d)

Exponential

44.

Find the inverse of f(x)=log₄(x+4)

a)

f^-1(x)=4^(x-4)

b)

f^-1(x)=4^x+4

c)

f^-1(x)=4^x-4

d)

f^-1(x)=4^x

45.

Find the inverse of f(x)=log₃(x+2)

a)

f^-1(x)=1^x

b)

f^-1(x)=3^x-2

c)

f^-1(x)=3^(x-2)

d)

f^-1(x)=3^(x+2)

46.

Find the inverse of y=9^x

a)

y=log_x9

b)

y=log₁₀9

c)

x=log_y9

d)

y=log₉x

47.

Find the inverse of $f\left(x\right)=3\cdot6^x-2$ .

a)

$f^{-1}\left(x\right)=3\cdot\log_x6$

b)

$f^{-1}\left(x\right)=\log_6\left(\frac{x+2}{3}\right)$

c)

$f'\left(x\right)=\log_{6x}$

d)

$f'\left(x\right)=\log\ \left(6+x\right)$

48.

Use the change of base rule to rewrite this problem:

log₅75

a)

log(75)/log(5)

b)

log(5)/log(75)

49.

Use the change of base rule to rewrite this problem:

log₆216

a)

log(6)/log(216)

b)

log(216)/log(6)

50.

Use the change of base rule to rewrite this problem:

log₇729

a)

log(7)/log(729)

b)

log(729)/log(7)

Logarithms

Total questions: 50

Worksheet time: 1hrs 15mins

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