Free Printable College Algebra Final REV CH 4 LOGS

1.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

2.

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

3.

Write in exponential form

log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

4.

Solve for x:
log_x25 = 2

a)

5

b)

-5

c)

1/5

d)

-1/5

5.

Solve for x.
3^x = 27

a)

2

b)

4

c)

3

d)

5

6.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

7.

Evaluate log₄1

a)

1

b)

0

c)

4

d)

undefined

8.

Use the change of base formula and your calculator to approximate the log.

a)

A

b)

B

c)

C

d)

D

9.

Use the change of base formula and your calculator to approximate the log.

a)

A

b)

B

c)

C

d)

D

10.

Rewrite the equation in logarithmic form.

a)

A

b)

B

c)

C

d)

D

11.

Rewrite the equation in logarithmic form.

a)

A

b)

B

c)

C

d)

D

12.

Expand the logarithm.

a)

A

b)

B

c)

C

d)

D

13.

Expand the logarithm.

a)

A

b)

B

c)

C

d)

D

14.

Expand the logarithm.

a)

A

b)

B

c)

C

d)

D

15.

Evaluate the following logarithm:

log₅5

a)

1

b)

0

c)

-1

d)

¹/₂

16.

Evaluate.
log₆(¹/₂₁₆)

a)

3

b)

¹/₃

c)

-¹/₃

d)

-3

17.

Evaluate the following logarithm:

log₄2

a)

-¹/₂

b)

-2

c)

2

d)

¹/₂

18.

Evaluate the following logarithm:

log₈√8

a)

-¹/₂

b)

-1

c)

1

d)

¹/₂

19.

Evaluate the following logarithm:

log₂₅0.2

a)

-¹/₂

b)

-2

c)

2

d)

¹/₂

20.

Evaluate the following logarithm:

log₁₂1

a)

1

b)

0

c)

-1

d)

¹/₂

21.

Evaluate the following logarithm:

log₁₅1

a)

1

b)

0

c)

-1

d)

¹/₂

22.

Evaluate the following logarithm:

log₃(¹/₃)

a)

-2

b)

-¹/₂

c)

-1

d)

¹/₂

23.

Evaluate the following logarithm:

log₄(¹/₆₄)

a)

3

b)

-¹/₃

c)

-3

d)

¹/₃

24.

Evaluate the following logarithm:

log₈₁27

a)

²/₃

b)

³/₂

c)

³/₄

d)

⁴/₃

25.

Evaluate the following logarithm:

log₆36

a)

3

b)

2

c)

1

d)

0

26.

log(4x)

a)

log4-logx

b)

log4+logx

c)

4logx

d)

xlog4

27.

log(xy²)

a)

logx+2logy

b)

logx+logy²

c)

logx-2logy

d)

logx+logy+log2

28.

$\log\left(\frac{x}{y}\right)$

a)

logx+logy

b)

xlogy

c)

log(x-y)

d)

logx-logy

29.

You want to solve for x. Which of these is the correct "step 1"?

a)

$\log_78=\log_7x$

b)

$\log_742=\log_7x$

c)

$\log_748=\log_7\left(\frac{x}{6}\right)$

d)

$\log_754=\log_7x$

30.

Finish solving for x

a)

x = 6

b)

x = 7

c)

x = 8

d)

x = 56

31.

We want to solve for x. What's the first step?

a)

Rewrite as a logarithm: $\log_{189}3=x$

b)

Rewrite as a logarithm: $\log_3189=x$

c)

Rewrite 189 with a base of 3: $3^x=3^{63}$

d)

Rewrite 189 with a base of 3: $3^x=3^9$

32.

Finish solving for x.

a)

0.210 = x

b)

5 = x

c)

63 = x

d)

4.771 = x

e)

4.462 = x

33.

Solve for x: $9^x=60$

a)

1.748

b)

x = 6.667

c)

x = 0.537

d)

x = 1.863

34.

Solve for x.
$\log_52+\log_5x=\log_520$
x = (a)

35.

Solve for x.
$2\log_410=\log_4\left(8x\right)+\log_4\left(5\right)$

a)

x = 2.5

b)

x = 0.5

c)

x = 1.538

d)

x = 11.875

36.

$5\log_yy-2\log_yy^{-3}$

a)

1

b)

11

c)

-1

d)

$\frac{5}{6}$

37.

Solve for x.

a)

$\frac{\log6-3\log3}{4\log3-2\log6}$

b)

$\frac{\log6+3\log3}{4\log3-2\log6}$

c)

$\frac{2\log6+\log6}{4\log3-3\log3}$

d)

no solution

38.

$4\log_2\left(2x+24\right)-17=-9$
Once you have isolated the log in the equation, what would be the next step?

a)

log both sides

b)

rewrite as an exponential

c)

nothing, you would not be able to solve it

d)

divide both sides by 2

39.

log₄(3x-1)=log₄(2x+3)

a)

4

b)

3

c)

1

d)

8

40.

log₈(4x+4)=2

a)

15

b)

12

c)

10

d)

3

41.

log₈₁x = 3/4

a)

2

b)

3

c)

27

d)

81

42.

Solve

\log x=1-\log\left(x-3\right)

a)

$-2$

b)

0

c)

3

d)

5

43.

Solve

2\log_4x+3\log_x4=7

a)

2

b)

4

c)

12

d)

64

44.

Solve

\log_5x+\log_x25=3

a)

5

b)

10

c)

25

d)

30

45.

Express as a single logarithm with base 4

a)

$0.792481$

b)

$\frac{1}{2}\cdot\log_2\left(3\right)$

c)

$\log_4\left(3\right)$

d)

$\log_4\left(\frac{9}{2}\right)$

46.

Solve

a)

$x=\frac{14}{3}$

b)

$x=5$

c)

$x=-5$

d)

No Solution

47.

Solve for x. Round your answer to 3 decimal places.

a)

$x=49.471$

b)

$x=33,333.333$

c)

$x=1.667$

d)

$x=0.6$

48.

a)

$x=27$

b)

$x=\left\{\pm27\right\}$

c)

$x=\left\{\pm\sqrt{\frac{4}{9}}\right\}$

d)

$x=\frac{2}{3}$

49.

Round to 3 decimal places if necessary.

a)

$x=.889$

b)

$x=2.101$

c)

$x=8.524$

d)

No Solution

50.

Express as a single logarithm.

a)

$\ln\left(\frac{5\cdot y}{x^3}\right)$

b)

$\ln\left(\frac{5}{x^3\cdot y}\right)$

c)

$\ln\left(5\cdot x^3\cdot y\right)$

d)

$\ln\left(5-3x+y\right)$

51.

Solve. Round your answer to 3 decimal places.

a)

1.348

b)

78.704

c)

15.728

d)

0.311

52.

Expand

a)

$\ln\left(18\right)+3\ln\left(x\right)+\ln\left(y\right)$

b)

$3\ln\left(18\right)+3\ln\left(x\right)+\ln\left(y\right)$

c)

$3\ln\left(18x\right)+\ln\left(y\right)$

d)

$3\ln\left(6x\right)+\ln\left(y\right)$

College Algebra Final REV CH 4 LOGS

Total questions: 52

Worksheet time: 4hrs 20mins

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