Quiz about Properties of logarithms Quiz

Question 1

$$\log_312$$
Which of the following is a possible expansion for this logarithm? Check all that apply.

Accepted Answer

$$\log_34+\log_33$$

Accepted Answer

$$\log_32+\log_36$$

Accepted Answer

$$\log_336-\log_33$$

Answer

$$\log_310+\log_32$$

Answer

$$\log_315-\log_33$$

Question 2

$$\log_324$$
Which of the following is a possible expansion for this logarithm? Check all that apply.

Accepted Answer

$$\log_34+\log_36$$

Accepted Answer

$$\log_348-\log_32$$

Accepted Answer

$$\log_38+\log_33$$

Answer

$$\log_34+\log_320$$

Answer

$$\log_310+\log_314$$

Question 3

Which of the logarithms below is equivalent to the following:
$$2\log12$$

Accepted Answer

log 144

Answer

log 10

Answer

log 6

Answer

log 24

Question 4

Evaluate $$\log_6\ \frac{1}{36}+\log_636-5^{\log_61}$$ . Use the table to approximate the value of the logarithmic expression or use the change-of-base formula to simplify.

Accepted Answer

$$1$$

Answer

$$5$$

Answer

$$12$$

Answer

$$0$$

Question 5

Use the properties of logarithms to rewrite as the sum of two logarithms:

$$\log55$$

Accepted Answer

log 11 + log 5

Answer

log 40 + log 15

Answer

log 50 + log 5

Question 6

Question 6.

Accepted Answer

log₈(x) + log₈(y) + 6log₈(z)

Answer

6log₈(xyz)

Answer

log₈(x) - log₈(y) - 6log₈(z)

Answer

log₈(x) + log₈(y) - log₈(z)

Question 7

Condense

Accepted Answer

D

Answer

A

Answer

B

Answer

C

Question 8

Question 8.

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 9

Rewrite as a single logarithm:

$$\log_260\ -\ \log_210$$

Accepted Answer

$$\log_26$$

Answer

$$\log_250$$

Answer

$$\frac{\log_260}{\log_210}$$

Answer

$$\log_270$$

Question 10

Expand

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 11

Using the change of base rule, what is this logarithm equivalent to?

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 12

Condense

Accepted Answer

logxyz3

Answer

log(xy/z³)

Answer

logx+logy+logz³

Answer

logx³y³z³

Question 13

Expand

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 14

Expand.

Accepted Answer

1/3 log x + 1/3 log y + 1/3 log z

Answer

1/3 log x + log y + log z

Answer

1/3 log x - 1/3 log y - 1/3 log z

Answer

3 log x + 3 log y + 3 log z

Question 15

Evaluate $$\log_330-\log_4\ 4^5$$ . Use the table to approximate the value of the logarithmic expression or use the change-of-base formula to simplify.

Accepted Answer

$$-1.9041$$

Answer

$$1.9041$$

Answer

$$19,041$$

Answer

$$9,041$$

Properties of logarithms Quiz

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