Free Printable Logarithm to Exponential and Vice Versa

1.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

2.

Rewrite log₂8 = 3 in exponential form.

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

3.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

4.

Change to Logarithmic Form:
5³ = 125

a)

log ₅ 125 = 3

b)

log₃125 = 5

c)

log ₅ 3 =125

d)

log₁₂₅ 3 = 5

5.

Rewrite log_vn = a in exponential form.

a)

v^a = n

b)

n^a = v

c)

vⁿ = a

d)

aⁿ = v

6.

Rewrite log₂8 = 3 in exponential form/

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

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.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

9.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

10.

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

11.

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)

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

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:
$12^2=144$

a)

$\log_{12}2=144$

b)

$\log_2144=12$

c)

$\log_{12}144=2$

d)

$\log_{144}12=2$

14.

Convert the exponential form $5^3 = 125$ into its equivalent logarithmic form.

a)

$\log_5{125} = 3$

b)

$\log_5{3} = 125$

c)

$\log_{125}{5} = 3$

d)

$\log_{3}{125} = 5$

15.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

16.

Convert the exponential form to logarithmic form: $2^3 = 8$

a)

$\log_2(8) = 3$

b)

$\log_8(2) = 3$

c)

$\log_3(2) = 8$

d)

$\log_2(3) = 8$

Logarithm to Exponential and Vice Versa

Total questions: 16

Worksheet time: 18mins

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