Free Printable Convert logarithms and exponentials

1.

Evaluate.

log₆(¹/₂₁₆) = x

a)

3

b)

¹/₃

c)

-¹/₃

d)

-3

2.

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

3.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

4.

What is the base of log₃(x) = 9?

a)

x

b)

3

c)

9

d)

3^x

5.

Rewrite the equation in logarithmic form.

a)

A

b)

B

c)

C

d)

D

6.

Rewrite in exponential form:
ln(2) = x

a)

2^x= 10

b)

10² = x

c)

e^x= 2

d)

e² = x

7.

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

8.

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

9.

The natural logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

10.

Rewrite each equation in logarithmic form.

a)

A

b)

B

c)

C

d)

D

11.

Rewrite log_vn = a in exponential form.

a)

v^a = n

b)

n^a = v

c)

vⁿ = a

d)

aⁿ = v

12.

Rewrite log₂8 = 3 in exponential form

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

13.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

14.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

15.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

16.

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

a)

$36^2=6$

b)

$2^6=36$

c)

$6^2=36$

d)

$2^{36}=6$

17.

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

a)

$4^3=81$

b)

$3^4=81$

c)

$81^3=4$

d)

$4^{81}=3$

18.

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

a)

$v^4=u$

b)

$4^v=u$

c)

$v^u=4$

d)

$u^4=v$

19.

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)

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

20.

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)

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

21.

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

a)

$\log_{12}2=144$

b)

$\log_2144=12$

c)

$\log_{12}144=2$

d)

$\log_{144}12=2$

22.

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)

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

23.

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

a)

$\log_a8=b$

b)

$\log_8a=b$

c)

$\log_ba=8$

d)

$\log_8b=a$

24.

Rewrite in logarithmic form:

18^2=324

a)

$\log_2\left(18\right)=324$

b)

$\log_2\left(324\right)=18$

c)

$\log_{18}\left(324\right)=2$

d)

$\log_{18}\left(2\right)=324$

25.

Rewrite the equation in logarithmic form.

a)

A

b)

B

c)

C

d)

D

26.

Rewrite the equation in logarithmic form.

a)

A

b)

B

c)

C

d)

D

27.

Rewrite the expression in logarithmic form.

$w^3=40$

a)

$\log_w40=3$

b)

$\log_{40}w=3$

c)

$\log_340=w$

d)

$\log_w3=40$

28.

Write in exponential form.
$\log_264\ =\ 6$

a)

$6^2=64$

b)

$2^6=64$

c)

$\frac{\log\left(64\right)}{\log\left(2\right)}$

d)

$\frac{\log\left(2\right)}{\log\left(64\right)}$

29.

$10^{-1}=\ \frac{1}{10}$

Write in logarithmic form.

a)

$10^{\frac{1}{10}}=\ -1$

b)

$\frac{1}{10}^{10\ }=\ -1$

c)

$\log_{\frac{1}{10}}=\ 10$

d)

$\log_{10}\ \left(\frac{1}{10}\right)=\ -1$

30.

Rewrite this equation in exponential form.

a)

b)

c)

d)

31.

Rewrite this equation in exponential form.

a)

b)

c)

d)

32.

Rewrite this equation in exponential form.

a)

b)

c)

d)

33.

Rewrite this equation in exponential form.

a)

b)

c)

d)

34.

Rewrite this equation in exponential form.

a)

b)

c)

d)

35.

Rewrite this equation in logarithmic form.

a)

b)

c)

d)

36.

Rewrite this equation in logarithmic form.

a)

b)

c)

d)

37.

Rewrite this equation in logarithmic form.

a)

b)

c)

d)

38.

Rewrite this equation in logarithmic form.

a)

b)

c)

d)

39.

Rewrite this equation in logarithmic form.

a)

b)

c)

d)

40.

Rewrite in exponential form:
ln(2) = x

a)

2^x= 10

b)

10² = x

c)

e^x= 2

d)

e² = x

Convert logarithms and exponentials

Total questions: 40

Worksheet time: 7hrs 40mins

Similar Resources on Wayground