Free Printable Logarithm Practice

1.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

2.

Evaluate.
log₆(¹/₂₁₆)

a)

3

b)

¹/₃

c)

-¹/₃

d)

-3

3.

Evaluate.
3 log₂4

a)

3

b)

6

c)

2

d)

4

4.

Evaluate.
3 log₈2

a)

¹/₃

b)

3

c)

1

d)

9

5.

Write in logarithmic form.
5² = 25

a)

log₅2 = 25

b)

log₂25 = 5

c)

log₂₅5 = 2

d)

log₅25 = 2

6.

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

7.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

8.

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

9.

Evaluate the following logarithm:

log₅5

a)

1

b)

0

c)

-1

d)

¹/₂

10.

Evaluate the following logarithm:

log₆36

a)

3

b)

2

c)

1

d)

0

11.

Evaluate the following logarithm:

log₂₇3

a)

¹/₃

b)

-3

c)

-¹/₂

d)

¹/₂

12.

Evaluate the following logarithm:

log₁₅1

a)

1

b)

0

c)

-1

d)

¹/₂

13.

Evaluate the following logarithm:

log₁₂1

a)

1

b)

0

c)

-1

d)

¹/₂

14.

Simplify the expression using the product rule of logarithms: $\log_b(x) + \log_b(y)$ .

a)

$\log_b(x \cdot y)$

b)

$\log_b(x + y)$

c)

$\log_b(\frac{x}{y})$

d)

$\log_b(x - y)$

15.

Use the quotient rule to simplify: $\log_c(35) - \log_c(7)$ .

a)

$\log_c(5)$

b)

$\log_c(42)$

c)

$\log_c(28)$

d)

$\log_c(\frac{35}{7})$

16.

Apply the product rule to find the value of $\log_2(8) + \log_2(4)$ .

a)

$\log_2(32)$

b)

$\log_2(12)$

c)

$\log_2(2)$

d)

$\log_2(24)$

17.

Simplify using the quotient rule: $\log_k(81) - \log_k(9)$ .

a)

$\log_k(9)$

b)

$\log_k(72)$

c)

$\log_k(\frac{81}{9})$

d)

$\log_k(8)$

18.

Apply the quotient rule to simplify: $\log_5(125) - \log_5(25)$ .

a)

$\log_5(100)$

b)

$\log_5(5)$

c)

$\log_5(\frac{125}{25})$

d)

$\log_5(1)$

19.

Condense: $4\log_5k-\log_5d$

a)

$\log_5k^4d$

b)

$\log_5\ 4kd$

c)

$\log_5\ \frac{k^4}{d}$

d)

$\log_5\ \frac{k}{d^4}$

20.

Condense: $7\log v\ +\ 3\log w$

a)

$\log\ \frac{v^7}{w^3}$

b)

$\log21vw$

c)

$\log v^7w^3$

d)

$10\log\ \frac{v}{w}$

21.

Choose the correct expanded natural logarithm:

$\ln\left(\frac{2x^2y}{z^4}\right)$

a)

$\ln2+2\ln x+\ln y+4\ln z$

b)

$\ln2+2\ln x+\ln y-4\ln z$

c)

$2\ln(2xy)-4\ln z$

d)

$2\ln2x+\ln y-4\ln z$

22.

Power Property:

$\log_b\left(m^n\right)=$

a)

$\log_b\left(m\right)+\log_b\left(n\right)$

b)

$\log_b\left(m\right)-\log_b\left(n\right)$

c)

$n\log_b\left(m\right)$

d)

$\frac{\log_b\left(m\right)}{\log_b\left(n\right)}$

e)

$\frac{\log_b\left(n\right)}{\log_b\left(m\right)}$

23.

$a^{\log_a\ n}=$

a)

$\log_ax+\log_ay$

b)

$\log_ax-\log_ay$

c)

$n$

d)

$a$

24.

$\log_a\ a\ =$

a)

Not defined

b)

0

c)

1

d)

$a$

25.

$\log_{x\ }\sqrt[]{x}\ =$

a)

1

b)

2

c)

$\frac{1}{2}$

d)

x

26.

Expand.
Log₅ x³/ y²

a)

A

b)

B

c)

C

d)

D

27.

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

28.

f(x)=log₅(x+4) - 2

Find the Domain and Range

a)

Domain: x ≥ -4

Range: all real numbers

b)

Domain: all real numbers

Range: y ≥ -4

c)

Domain: all real numbers

Range: y > -4

d)

Domain: x > -4

Range: all real numbers

29.

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

30.

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

31.

What is the transformation of the logarithmic function
$f\left(x\right)=\log\ \left(x+3\right)-1$

a)

left 3, right 1

b)

right 3, down 1

c)

right 3, up 1

d)

left 3, down 1

32.

Which graph matches the logarithmic equation

a)

b)

c)

d)

33.

Describe domain of the function shown: y=log₂(x+1)

a)

(-∞,∞)

b)

(-1,∞)

c)

(-1,3)

d)

(∞, -1)

34.

Describe the transformations of f(x)= -log₂(x+1)

a)

left one & y-axis reflection

b)

right one & y-axis reflection

c)

left one & x-axis reflection

d)

right one & x-axis reflection

35.

Which of the following transformations would take f(x)= lnx to g(x)= −ln(x+5)

a)

reflection over the x-axis

b)

reflection over the y-axis

c)

translate right 5

d)

translate up 5

e)

translate left 5

36.

Describe the transformation of y=ln(x) that would give the graph for y = 7ln(x)

a)

vertical translation 7 up

b)

vertical stretch by a factor of 7

c)

vertical compression by a factor of 7

d)

horizontal translation 7 left

37.

Logarithmic functions are the inverse of _________________

a)

exponential functions

b)

linear functions

c)

quadratic functions

d)

cubic functions

38.

f(x)=¼ ln(x - 2) + 3 Describe the transformation

a)

Vertical Stretch by 1/4, translation 2 units right, 3 units up

b)

Vertical Compression by 1/4, translation 2 units right, 3 units up

c)

Vertical Stretch by 1/4, translation 2 units left, 3 units up

d)

Vertical Compression by 1/4, translation 2 units left, 3 units up

39.

Match the graph with its equation

a)

y = log₄ (x)+2

b)

y = log₄ (x + 2) + 1

c)

y = log₄ (x - 1) + 2

d)

y = log₄ (-x + 2)

40.

Match the graph with its equation

a)

y = log₆(-x) + 1

b)

y = log₆(x − 2) + 1

c)

y = log₆(x + 2) - 1

d)

y = log(x-8) + 1

Logarithm Practice

Total questions: 40

Worksheet time: 48mins

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