Quiz about Logarithm Practice

Question 1

Evaluate.
log₃81

Accepted Answer

4

Answer

1/4

Answer

-4

Answer

-1/4

Question 2

Evaluate.
log₆(¹/₂₁₆)

Accepted Answer

-3

Answer

3

Answer

1/3

Answer

-1/3

Question 3

Evaluate.
3 log₂4

Accepted Answer

6

Answer

3

Answer

2

Answer

4

Question 4

Evaluate.
3 log₈2

Accepted Answer

1

Answer

1/3

Answer

3

Answer

9

Question 5

Write in logarithmic form.
5² = 25

Accepted Answer

log₅25 = 2

Answer

log₅2 = 25

Answer

log₂25 = 5

Answer

log₂₅5 = 2

Question 6

Write in logarithmic form.
2^-4 = ¹/₁₆

Accepted Answer

log₂(¹/₁₆) = -4

Answer

log_-4(¹/₁₆) = 2

Answer

log_-4 2 = ¹/₁₆

Answer

log₂(-4) = ¹/₁₆

Question 7

Write in exponential form.
log₂32 = 5

Accepted Answer

25 = 32

Answer

2-5 = 32

Answer

232 = 5

Answer

325 = 2

Question 8

Write in exponential form.
log₂(¹/₈) = -3

Accepted Answer

2^-3 = ¹/₈

Answer

21/8 = -3

Answer

-3² = ¹/₈

Answer

-31/8 = 2

Question 9

Evaluate the following logarithm:

log₅5

Accepted Answer

1

Answer

0

Answer

-1

Answer

1/2

Question 10

Evaluate the following logarithm:

log₆36

Accepted Answer

2

Answer

3

Answer

1

Answer

0

Question 11

Evaluate the following logarithm:

log₂₇3

Accepted Answer

1/3

Answer

-3

Answer

-1/2

Answer

1/2

Question 12

Evaluate the following logarithm:

log₁₅1

Accepted Answer

0

Answer

1

Answer

-1

Answer

1/2

Question 13

Evaluate the following logarithm:

log₁₂1

Accepted Answer

0

Answer

1

Answer

-1

Answer

1/2

Question 14

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

Accepted Answer

$$\log_b(x \cdot y)$$

Answer

$$\log_b(x + y)$$

Answer

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

Answer

$$\log_b(x - y)$$

Question 15

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

Accepted Answer

$$\log_c(5)$$

Answer

$$\log_c(42)$$

Answer

$$\log_c(28)$$

Answer

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

Question 16

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

Accepted Answer

$$\log_2(32)$$

Answer

$$\log_2(12)$$

Answer

$$\log_2(2)$$

Answer

$$\log_2(24)$$

Question 17

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

Accepted Answer

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

Answer

$$\log_k(9)$$

Answer

$$\log_k(72)$$

Answer

$$\log_k(8)$$

Question 18

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

Accepted Answer

$$\log_5(5)$$

Answer

$$\log_5(100)$$

Answer

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

Answer

$$\log_5(1)$$

Question 19

Condense: $$4\log_5k-\log_5d$$

Accepted Answer

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

Answer

$$\log_5k^4d$$

Answer

$$\log_5\ 4kd$$

Answer

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

Question 20

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

Accepted Answer

$$\log v^7w^3$$

Answer

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

Answer

$$\log21vw$$

Answer

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

Question 21

Choose the correct expanded natural logarithm:

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 22

Power Property:

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Answer

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

Question 23

$$a^{\log_a\ n}=$$

Accepted Answer

$$n$$

Answer

$$\log_ax+\log_ay$$

Answer

$$\log_ax-\log_ay$$

Answer

$$a$$

Question 24

$$\log_a\ a\ =$$

Accepted Answer

1

Answer

Not defined

Answer

0

Answer

$$a$$

Question 25

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

Accepted Answer

$$\frac{1}{2}$$

Answer

1

Answer

2

Answer

x

Question 26

Expand.
Log₅ x³/ y²

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 27

f(x)=log₅(x+4) - 2

Describe the asymptote

Accepted Answer

Vertical Asymptote x = -4

Answer

Horizontal Asymptote x = -4

Answer

Horizontal Asymptote x = 4

Answer

Vertical Asymptote x = 4

Question 28

f(x)=log₅(x+4) - 2

Describe the transformation

Accepted Answer

translation 4 units to the left, 2 units down

Answer

translation 4 units to the right, 2 units down

Answer

translation 4 units to the up, 2 units right

Answer

translation 4 units to the up, 2 units left

Question 29

Which graph matches the logarithmic equation

Accepted Answer

Option C is correct

Answer

A.

Answer

B.

Answer

D.

Question 30

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

Accepted Answer

left one & x-axis reflection

Answer

left one & y-axis reflection

Answer

right one & y-axis reflection

Answer

right one & x-axis reflection

Question 31

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

Accepted Answer

vertical stretch by a factor of 7

Answer

vertical translation 7 up

Answer

vertical compression by a factor of 7

Answer

horizontal translation 7 left

Question 32

Logarithmic functions are the inverse of _________________

Accepted Answer

exponential functions

Answer

linear functions

Answer

quadratic functions

Answer

cubic functions

Question 33

Match the graph with its equation

Accepted Answer

y = log₄ (x + 2) + 1

Answer

y = log₄ (x)+2

Answer

y = log₄ (x - 1) + 2

Answer

y = log₄ (-x + 2)

Logarithm Practice

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