Free Printable Logarithms

1.

Condense the Logarithm $5\log_{ }a\ -\ 25\log_{ }b$

a)

$\log\ \left(a^5+b^{25}\right)$

b)

$\log\ \left(a^5-b^{25}\right)$

c)

$\log\ \left(ab\right)^{25}$

d)

$\log_{ }\ \left(\frac{a^5}{b^{25}}\right)$

2.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

3.

Write as a single logarithm:

log(30)-log(6)

a)

-6log(30)

b)

log(24)

c)

log(-24)

d)

log(5)

4.

Rewrite in exponential form:
ln(2) = x

a)

2^x= 10

b)

10² = x

c)

e^x= 2

d)

e² = x

5.

6^-3x=216

a)

x=3

b)

x=-1

c)

x=6

d)

x=-3

6.

Write as one logarithm. Simplify, if possible.
log₅125 - log₅25

a)

1

b)

0

c)

5

d)

-1

7.

Write as one logarithm. Simplify, if possible.
log₆3 + log₆2

a)

0

b)

log₆5

c)

log₆1

d)

1

8.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

9.

Evaluate.
log₆(¹/₂₁₆)

a)

3

b)

¹/₃

c)

-¹/₃

d)

-3

10.

Evaluate.
3 log₂4

a)

3

b)

6

c)

2

d)

4

11.

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

12.

f(x)=log₅(x+4) - 2

Describe the transformation

a)

translation 4 units to the right, 2 units down

b)

translation 4 units to the left, 2 units down

c)

translation 4 units to the up, 2 units right

d)

translation 4 units to the up, 2 units left

13.

f(x)=2ln(x+2)

Describe the transformation

a)

Vertical Stretch by 2, translation 2 units to the left

b)

Vertical Compression by 2, translation 2 units to the left

c)

Vertical Stretch by 2, translation 2 units to the right

d)

Vertical Compression by 2, translation 2 units to the right

14.

What is the asymptote of y = 2^x ?

a)

y = 0

b)

x = 0

15.

What is the asymptote of y = 2^x - 3

a)

y = 0

b)

y = -3

c)

x = 0

d)

x = -3

Logarithms

Total questions: 15

Worksheet time: 10mins

Similar Resources on Wayground