Free Printable MC 9.3+9.4- Evaluating Logs and their properties Alg 2

1.

log ₃9 =

a)

1/2

b)

2

c)

1/3

d)

3

2.

log ₂₅ 5 =

a)

1/2

b)

2

c)

1/5

d)

5

3.

log ₁₆ 8 =

a)

1/2

b)

4/3

c)

2

d)

3/4

4.

log ₉ 27 =

a)

3

b)

2/3

c)

3/2

d)

1/3

5.

log 1000 =

a)

1/10

b)

10

c)

1/3

d)

3

6.

log (1/10,000)

a)

1/4

b)

-4

c)

1000

d)

-1000

7.

log _a a =

a)

10

b)

0

c)

1

d)

-1

8.

log ₉ (1/3) =

a)

-1/2

b)

-2

c)

-3

d)

-1/3

9.

log ₂₅(1/125)

a)

-1/5

b)

5

c)

-3/2

d)

2/3

10.

log ₃₂ 4 =

a)

1/8

b)

8

c)

5/2

d)

2/5

11.

log ₂16

a)

3

b)

2

c)

4

d)

5

12.

log ₃ 27

a)

4

b)

2

c)

5

d)

3

13.

log ₁₇ 1

a)

1

b)

0

c)

17

d)

18

14.

Write equation in exponential form. $\log_2128=7$

a)

$7^2=128$

b)

$2^7=128$

c)

$128^2=7$

d)

$2^{128}=7$

15.

Write equation in exponential form. $\log_864=2$

a)

$2^8=64$

b)

$64^8=2$

c)

$8^2=64$

d)

$2^{64}=8$

16.

Write equation in exponential form. $\log_3\frac{1}{27}=-3$

a)

$-3^3=\frac{1}{27}$

b)

$\frac{1}{27}^3=-3$

c)

$\frac{1}{27}^{-3}=3$

d)

$3^{-3}=\frac{1}{27}$

17.

Write the equation in logarithmic form. $4^4=256$

a)

$\log_44=256$

b)

$\log_{256}4=4$

c)

$\log_4256=4$

d)

$\log4=256$

18.

Write the equation in logarithmic form. $8^3=512$

a)

$\log_38=512$

b)

$\log_8512=3$

c)

$\log_3512=8$

d)

$\log_{512}8=3$

19.

$\log\left(\frac{8x}{yz}\right)\$

a)

log8+logx-logy-logz

b)

log8+logx-logy+logz

c)

log(8x)-log(yz)

d)

8logx-ylogz

20.

Rewrite log_b(xⁿ)

a)

nlog_bx

b)

(log_bx)ⁿ

c)

xⁿlog_bx

d)

log_b(xⁿ)

21.

Condense: log16 + log2 - log8

a)

log4

b)

log8

c)

log10

d)

log24

22.

Use multiple log properties to write as a single log:
log₂x - 5log₂y

a)

log₂(x/y⁵)

b)

log₂(xy⁵)

c)

log₂(x/y)⁵

d)

log₂(x/5y)

23.

log(3x)²

a)

2log(3+x)

b)

2log3+logx

c)

log3+2logx

d)

2(log3+logx)

24.

log(xy²)

a)

logx+2logy

b)

logx+logy²

c)

logx-2logy

d)

logx+logy+log2

25.

log(4x)

a)

log4-logx

b)

log4+logx

c)

4logx

d)

xlog4

26.

When you have two log expressions separated by a minus sign (-), we really need to ___________ them to simplify into one log expression.

a)

add

b)

subtract

c)

multiply

d)

divide

27.

When you have two log expressions separated by a plus sign (+), we really need to ___________ them to simplify into one log expression.

a)

add

b)

subtract

c)

multiply

d)

divide

28.

$\log\left(\frac{4}{5}\right)$ Expand the Log

a)

$\log4\ +\log5$

b)

$\log\ 20$

c)

$\log4\ -\log5$

29.

a)

log(x) + log(z) + 4log(y)

b)

3log(x) − log(z) − 4log(y)

c)

3log(x) + log(z) + 4log(y)

d)

log(x) − 4log(z) − 3log(y)

30.

Simplify: $\log_4\left(x+4\right)-\log_4\left(x-5\right)$

a)

$\log_49$

b)

$\log_4\left(2x-1\right)$

c)

$\log_4\left(x^2-x-20\right)$

d)

$\log_4\left(\frac{x+4}{x-5}\right)$

31.

Evaluate the logarithm. Type in the number only for the answer.

$\log_636$

(a)

32.

Evaluate the logarithm. Type in the number only for the answer.

$\log_{243}27$

(a)

33.

Evaluate the logarithm. Type in the number only for the answer.

$\log_{16}8$

(a)

34.

Evaluate the logarithm. Type in the number only for the answer. Use Change of Base Formula, round to 2 decimal places.

$\log_735$

(a)

35.

Evaluate the logarithm. Type in the number only for the answer. Use Change of Base Formula, round to 2 decimal places.

$\log_2260$

(a)

36.

Evaluate the logarithm. Type in the number only for the answer. Use Change of Base Formula, round to 2 decimal places.

$\log_538$

(a)

37.

Expand the logarithm.
$\log\frac{x}{y^6}$

a)

$\log x+6\log y$

b)

$\log x-6\log y$

c)

$\log x+\log6y$

d)

$\log x-\log6y$

38.

Expand

a)

log₈x + log₈y + log₈z

b)

5log₈x + 5log₈y + 5log₈z

c)

log₈xy + 5log₈z

d)

log₈x + log₈y + 5log₈z

39.

Expand the logarithm. $\log_4\sqrt{x^3y}$

a)

$\frac{1}{2}\log_4\left(x\right)-\frac{1}{2}\log_4\left(y\right)$

b)

$\frac{3}{2}\log_4\left(x\right)+\frac{1}{2}\log_4\left(y\right)$

c)

$\frac{1}{2}\log_4\left(x\right)+\log_4\left(y\right)$

d)

$\frac{3}{2}\log_4\left(x\right)-\log_4\left(y\right)$

40.

Simplify: $3\log_92+\log_9x$

a)

$\log_9\left(32x\right)$

b)

$\log_9\left(8x\right)$

c)

$\log_9\left(\frac{8}{x}\right)$

d)

$\log_98x$

41.

Expand using the properties of Logaritms $\log_{ }\ \frac{x^3}{y^4z}$

a)

$\log_{ }x+4\log_{ }y\ +\log_{ }z$

b)

$3\log_{ }x-4\log_{ }y\ -\log_{ }z$

c)

$3\log_{ }x+4\log_{ }y\ +\log_{ }z$

d)

$3\log_{ }x-4\log_{ }y\ +\log_{ }z$

MC 9.3+9.4- Evaluating Logs and their properties Alg 2

Total questions: 41

Worksheet time: 53mins

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