Free Printable Math 3: Module 2 Test

1.

Evaluate: $\log_9729$

a)

3

b)

-1

c)

1

d)

0

e)

321

2.

Evaluate: $\log_{321}321$

a)

3

b)

-1

c)

1

d)

0

e)

321

3.

Evaluate: $\log_xx^{321}$

a)

3

b)

-1

c)

1

d)

0

e)

321

4.

Evaluate: $\log_3\ \frac{1}{3}$

a)

3

b)

-1

c)

1

d)

0

e)

321

5.

Evaluate: $\log_51$

a)

3

b)

-1

c)

1

d)

0

e)

321

6.

Evaluate.

3 log₂4

a)

3

b)

6

c)

2

d)

4

7.

Which of the following statements is false?

a)

$\log_90=0\ \ \ \$ because $9^0=0$

b)

$\log_39\ =2\ \ \ \ \ \$ because $3^2=\ 9$

c)

$\log_55=1\ \ \ \ \ \$ because $5^1=5$

d)

$\log_40$ does not exist because $4^x\ne0$

8.

Estimate: $\log_318$

a)

6

b)

between 5 & 6 about 5.6

c)

about 3.6

d)

between 2 & 3 about 2.6

9.

Estimate: $\log_354$

a)

18

b)

between 5 & 6, about 5.6

c)

between 3 & 4, about 3.6

d)

between 2 & 3, about 2.6

10.

Condense to a single logarithm.

a)

b)

c)

d)

11.

Condense

a)

log xyz³

b)

log(xy/z³)

c)

log x+log y+log z³

d)

log x³y³z³

12.

Expand each logarithmic expression: $\log_3\left(\frac{2}{a}\right)$

a)

$2+\log_3a$

b)

$\log_32\ +2\log_3a$

c)

$2\log_3a+2$

d)

$\log_32-\log_3a$

e)

$\log_3a-\log_32$

13.

Expand

a)

A

b)

B

c)

C

d)

D

14.

Expand

a)

6log₈v-2log₈u

b)

6log₈u-2log₈v

c)

3log₈u-2log₈v

d)

6log₈u+2log₈v

15.

Expand each logarithmic expression: $\log_32a^2$

a)

$2+\log_3a$

b)

$\log_32\ +2\log_3a$

c)

$2\log_3a+2$

d)

$\log_32-\log_3a$

e)

$\log_3a-\log_32$

16.

If $\log_x125\ =\ 3,\ \ \ \ then\ x\ =\$

(a)

17.

$\log_8\ \left(4x+4\right)\ =\ 2$

(a)

18.

$\log_4\ v+6=\ \log_4\ \ 3v\ -2$

(a)

19.

$4^{2x+3}=1$

(a)

20.

$9^{2x}=27^{-4+2x}$

(a)

21.

Describe the shift of $y\ =\ -2\ +\log_3\left(x\right)$

a)

left 2

b)

right 2

c)

down 2

d)

up 2

22.

Describe the shift of $y\ =\ 5\ +\ \log_3\left(x-1\right)$

a)

Right 1 Up 5

b)

Right 1 Down 5

c)

Left 1 Up 5

d)

Left 1 Down 5

23.

What is the Vertical Asymptote for the graph $y=3+\log_2\left(x-1\right)$

a)

x = -1

b)

x = 1

c)

x = 3

d)

x = -3

24.

Expand

a)

log₇x + log₇y + 4log₇z

b)

4log₇x + 4log₇y + 4log₇z

c)

log₇x - log₇y - 4log₇z

d)

4log₇x - 4log₇y - 4log₇z

25.

Condense

a)

log₈(a¹⁸/b³)

b)

log₈(a¹⁸b³)

c)

log₈(a/b³)

d)

15log₈(a/b³)

26.

Rewrite in Logarithm Form

a)

A

b)

B

c)

C

d)

D

27.

Rewrite in Exponential Form

a)

A

b)

B

c)

C

d)

D

28.

Condense the following expression into a single logarithm:
$2\log\left(a\right)+4\log\left(b\right)-9\log\left(c\right)$

a)

$\log\left(a^2b^4c^9\right)$

b)

$\log\left(a^2+b^4-c^9\right)$

c)

$\log\left(\frac{a^2b^4}{c^9}\right)$

d)

$\log\left(\frac{a^2}{b^4c^9}\right)$

29.

Condense the following expression into a single logarithm: $\log_58+\log_52$

a)

$\log_54$

b)

$\log_56$

c)

$\log_510$

d)

$\log_516$

30.

Expand each Logarithm $\log_39a$

a)

$2\ +\ \log_3a$

b)

$\log_32\ +\ 2\log_3a$

c)

$2\log_3a\ +\ 2$

d)

$\log_32\ -\ \log_3a$

e)

$\log_3a\ -\ \log_32$

Math 3: Module 2 Test

Total questions: 30

Worksheet time: 46mins

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