Free Printable Logarithmic and Exponential Equations

1.

How are exponential and logarithmic functions related?

a)

Opposites

b)

Inverses

c)

Cousins

d)

Reciprocals

2.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

3.

Write 10⁴= 10000 in logarithmic form.

a)

log₁₀ 4 = 10000

b)

log₁₀₀₀₀ 4 = 10

c)

log₁₀ 10000 = 4

d)

log₄ 10000 = 10

4.

Convert 10^(x+5)=100 to logarithmic form.

a)

log₁₀₀=x+5

b)

log(x+5)=100

c)

log(100)=x+5

d)

log_(x+5)(100)=10

5.

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

6.

Convert to logarithmic form: $3^7=y$

a)

$\log_3y=7$

b)

$\log_73=y$

c)

$\log_y3=7$

d)

$\log_37=y$

7.

Rewrite the equation in logarithmic form:
$12^2=144$

a)

$\log_{12}2=144$

b)

$\log_2144=12$

c)

$\log_{12}144=2$

d)

$\log_{144}12=2$

8.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

9.

Rewrite the equation in logarithmic form:
$8^b=a$

a)

$\log_a8=b$

b)

$\log_8a=b$

c)

$\log_ba=8$

d)

$\log_8b=a$

10.

Convert 6^(x+2)=216 to logarithmic form

a)

log₂₁₆(x+2)=6

b)

log₆(x+2)=216

c)

log₆(216)=x+2

d)

log_(x+2)(216)=6

11.

Convert 2^x+6=10 to logarithmic form

a)

log₄(x)=2

b)

log₂(4)=x

c)

log₂(10)=6

d)

log₂(x)=4

12.

Rewrite the equation in logarithmic form:
$9^{-2}=\frac{1}{81}$

a)

$\log_29=\frac{1}{81}$

b)

$\log_9\ \left(-2\right)=\frac{1}{81}$

c)

$\log_2\ \left(\frac{1}{81}\right)=9$

d)

$\log_9\ \frac{1}{81}=-2$

13.

Rewrite the equation in logarithmic form:
$64^{\frac{1}{2}}=8$

a)

$\log_{64}8=\frac{1}{2}$

b)

$\log_864=\frac{1}{2}$

c)

$\log_{64}\ \frac{1}{2}=8$

d)

$\log_8\ \frac{1}{2}=64$

14.

Convert log(x)=5 to exponential form

a)

1⁵=x

b)

10^x=5

c)

x⁵=10

d)

10⁵=x

15.

Rewrite the equation in exponential form:
$\log_vu=4$

a)

$v^4=u$

b)

$4^v=u$

c)

$v^u=4$

d)

$u^4=v$

16.

Convert to exponential form: $\log_216=4$

a)

$2^{16}=4$

b)

$4^2=16$

c)

$2^4=16$

d)

$16^2=4$

17.

Rewrite in exponential form: (remember base 10!)

log(7) = x

a)

7= 10^x

b)

10⁷ = x

c)

e^x= 7

d)

e⁷ = x

18.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

19.

Convert to exponential form: $\log10,000=4$

a)

$e^4=10,000$

b)

$4^e=10,000$

c)

$10^4=10,000$

d)

$4^{10}=10,000$

20.

Write in exponential form:
log ₃₆ 1 = 0

a)

36⁰ = 1

b)

36¹ = 0

c)

1³⁶ = 0

d)

1⁰ = 36

21.

Convert log₈(x+2)=3 to exponential form.

a)

8^(x+2)=3

b)

3^(x+2)=8

c)

8³=x+2

d)

3⁸=x+2

22.

Write in exponential form:

log ₂ 32 = 5

a)

2⁵ = 32

b)

5² = 32

c)

5³² = 2

d)

2³² = 5

23.

Convert log(x)=y+2 to exponential form.

a)

10^(y+2)=x

b)

1^x=y+2

c)

10^x=y+2

d)

x^(y+2)=10

24.

Convert log₁₂(x)=2 to exponential form.

a)

12²=x

b)

12^x=2

c)

x²=12

d)

2^x=12

25.

Rewrite the following equation in exponential form:
$\log_636=2$

a)

$36^2=6$

b)

$2^6=36$

c)

$6^2=36$

d)

$2^{36}=6$

26.

Rewrite the following equation in exponential form:
$\log_381=4$

a)

$4^3=81$

b)

$3^4=81$

c)

$81^3=4$

d)

$4^{81}=3$

27.

Rewrite the equation in exponential form:
$\log_{289}17=\frac{1}{2}$

a)

$17^{\frac{1}{2}}=289$

b)

$\frac{1}{2}^{17}=289$

c)

$289^{17}=\frac{1}{2}$

d)

$289^{\frac{1}{2}}=17$

28.

Solve for x.
log_x(64)=3

a)

x=8

b)

x=4

c)

x=3

d)

x=64

29.

Rewrite in exponential form.

a)

A

b)

B

c)

C

d)

D

30.

Rewrite the equation in logarithmic form.

a)

A

b)

B

c)

C

d)

D

31.

Solve for x: log 1 = x

a)

x = 2

b)

x = 3

c)

x = 4

d)

x = 0

32.

Solve for x: log 1000 = x

a)

x = 2

b)

x = 3

c)

x = 4

d)

x = 1

33.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

34.

Rewrite in exponential form:

log₃(9)=2.

a)

3⁹=2

b)

3²=9

c)

x²=9

d)

3^x=2

35.

Rewrite the equation into logarithmic form:

6² = 36

a)

log₆ 2 = 36

b)

log₆ 36 = 2

c)

ln 36 = 2

d)

6³⁶ = 2

36.

Change to Logarithmic Form:

5³ = 125

a)

log ₅ 125 = 3

b)

log₃125 = 5

c)

log ₅ 3 =125

d)

log₁₂₅ 3 = 5

37.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

38.

Write log₂ 0.25 = -2 in exponential form

a)

-2²= 0.25

b)

-2^0.25= 2

c)

2^-2= 0.25

d)

No correct answer

39.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

40.

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

41.

Rewrite log_vn = a in exponential form.

a)

v^a = n

b)

n^a = v

c)

vⁿ = a

d)

aⁿ = v

42.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

43.

Rewrite in exponential form:
2=log₉x

a)

9^x=2

b)

2^x=9

c)

2⁹=x

d)

9²=x

44.

Write 6^x = 8 in log form.

a)

log₆ 8 = x

b)

log₈ 6 = x

c)

log₆ x = 8

d)

log₈ x = 6

45.

Write log5 = x in exponential form

a)

10^x = 5

b)

5^x = 1

c)

1^x = 5

d)

10⁵ = x

46.

Write 10 = 5^x in log form

a)

x = log 5

b)

x = log₅10

c)

x = 5 log10

d)

x = 10 log 5

47.

Rewrite log₃t = 5 in exponential form.

a)

5^t=3

b)

log₃5 = log₃t

c)

t⁵=3

d)

3⁵=t

48.

Write in logarithmic form:

a^b = c

a)

log _a c = b

b)

log _b c = a

c)

log _a b = c

d)

log _b a = c

49.

Change to logarithmic form.

3^h = w

a)

log_w3 = h

b)

log₃w = h

c)

log_h3 = w

d)

log₃h = w

50.

Rewrite log₂8 = 3 in exponential form

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

51.

Write in exponential form:
log 100 = 2

a)

10² = 100

b)

2¹⁰ = 100

c)

100² = 10

d)

100¹⁰ = 2

52.

Convert 3^x = 12 to the equivalent log form.

a)

3¹² = x

b)

log_x3 = 12

c)

log₃x = 12

d)

log₃ 12 = x

53.

Write in logarithmic form:
2^-1 = 0.5

a)

log ₂ 0.5 = -1

b)

log _-1 0.5 = 2

c)

log ₂ -1 = 0.5

d)

log _-1 2 = 0.5

54.

Write in logarithmic form:
10²³ = 0.001

a)

log ₁₀ 0.001 = 23

b)

log ₂₃ 0.001 = 10

c)

log ₁₀ 23 = 0.001

d)

log ₂₃ 10 = 0.001

55.

Rewrite in logarithmic form. 7⁰=1

a)

log₀7=1

b)

log₇0=1

c)

log₇1=0

d)

log₁7=0

56.

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

57.

Re-write in exponential form log₅625=4

a)

5⁶²⁵=4

b)

5⁴=625

c)

4⁵=625

d)

4²=16

58.

Evaluate log₈ 8 by thinking 8 to what power is 8, so the answer is

a)

8

b)

-1

c)

0

d)

1

59.

Evaluate by thinking 4 to what power is 16, so

log₄16

a)

2

b)

4

c)

1/2

d)

-2

60.

log₅25 = ?

a)

2

b)

5

c)

125

Logarithmic and Exponential Equations

Total questions: 60

Worksheet time: 2hrs 34mins

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