Free Printable Unit 7 Review

1.

Simplify

a)

b)

c)

d)

2.

What is the base in the expressions.

a)

3

b)

7

c)

-3

d)

-7

3.

What is the exponent in the expressions?

a)

1

b)

2

c)

8

d)

1/8

4.

What is the base in the expressions.

a)

1

b)

2

c)

8

d)

1/8

5.

Solve

a)

-4

b)

5

c)

-3

d)

-5

6.

Solve

a)

-2

b)

6

c)

9

d)

3

7.

Solve

a)

-1/3

b)

-3

c)

-1

d)

3

8.

Solve

a)

2

b)

-2

c)

3

d)

-3

9.

Solve: 2^x = 4^x+1

a)

x = -2

b)

x = 2

c)

x = -3

d)

x = 3

10.

Solve: 9^8-x = 27^x-3

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

11.

Sovle for x:
5^{-3x - 1} = 25

a)

x = -1

b)

x = -4

c)

x = -3

d)

x = 1

12.

To solve 36 = 6^x, re-write 36 as what base and exponent?

a)

3⁶

b)

6³

c)

6²

d)

3¹²

13.

To solve 8 = 2^5x+7, you would need to re-write 8 as what base?

a)

8

b)

4

c)

2

d)

Cannot be determined

14.

Solve 3³ = 3^{4x + 2}

a)

¼

b)

-¼

c)

½

d)

-½

15.

Solve for n:
2^-2n = 2⁶

a)

-1

b)

-7

c)

5

d)

-3

16.

Solve for p:
4^p+2 = 64

a)

-16/9

b)

1

c)

8

d)

7/6

17.

Solve 3³ = 3^{4x + 2}

a)

x = ¼

b)

x = -¼

c)

x = ½

d)

x = -½

18.

log₃81 =

a)

2

b)

3

c)

4

d)

5

19.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

20.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

21.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

22.

Write the exponential equation as a logarithm
6³=216

a)

log₆(3) = 216

b)

log₃(6) = 216

c)

log₆(216)=3

d)

log₂₁₆(6)=3

23.

Rewrite in logarithmic form. 9^3/2=27

a)

log₉27=3/2

b)

log₉27=2/3

c)

log_3/29=27

d)

log₂₇9=3/2

24.

Rewrite in exponential form:
log (x) = ¼

a)

x^1/4 = 1

b)

1^x=¼

c)

10^1/4 = x

d)

10^x = ¼

25.

Rewrite in exponential form:
ln(2) = x

a)

2^x= 10

b)

10² = x

c)

e^x= 2

d)

e² = x

26.

Rewrite log₂8 = 3 in exponential form

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

27.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

28.

The natural logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

29.

Write in logarithmic form:
2^-1 = 0.5

a)

log ₂ 0.5 = -1

b)

log _-1 0.5 = 2

c)

log ₂ -1 = 0.5

d)

log _-1 2 = 0.5

30.

Write in logarithmic form:
10^-6 = .000001

a)

log(1) = 0

b)

log₁₀(10) = 1

c)

log₁₀(0.0001) = -6

d)

log(0.000001) = -6

31.

Rewrite the equation in logarithmic form.

a)

A

b)

B

c)

C

d)

D

32.

Rewrite log_x95 = 2.3

a)

x^2.3 = 95

b)

95^2.3 = x

c)

2.3⁹⁵ = x

d)

x⁹⁵= 2.3

33.

a)

ln(wvu⁵)

b)

ln(u + v + w⁵)

c)

ln(uvw⁵)

d)

ln(uvw)⁵

34.

Write the exponential equation as a logarithm
6³=216

a)

log₆(3) = 216

b)

log₃(6) = 216

c)

log₆(216)=3

d)

log₂₁₆(6)=3

35.

Rewrite the given expression as a logarithm.

a)

A

b)

B

c)

C

d)

D

36.

Rewrite this equation in logarithmic form.

a)

b)

c)

d)

37.

Rewrite this equation in logarithmic form.

a)

b)

c)

d)

38.

Rewrite the equation in logarithmic form.

a)

A

b)

B

c)

C

d)

D

39.

Rewrite in exponential form.

a)

A

b)

B

c)

C

d)

D

40.

Rewrite 1.6^(x+2) = 14.1

a)

log_1.614.1 = x+2

b)

log_1.6(x+2) = 14.1

c)

log_14.1(x+2) = 1.6

d)

log_(x+2)1.6 = 14.1

41.

Rewrite as a log: x = 11^y

a)

log₁₁(y) = x

b)

log_y(11) = x

c)

log₁₁(x) = y

d)

log_x(y) = 11

42.

Rewrite this equation in exponential form.

a)

b)

c)

d)

43.

a)

A

b)

B

c)

C

d)

D

44.

a)

A

b)

B

c)

C

d)

D

45.

log₈(xyz)

a)

6log₈(xyz)

b)

log₈(x) - log₈(y) - 6log₈(z)

c)

log₈(x) + log₈(y) - log₈(z)

d)

log₈(x) + log₈(y) + 6log₈(z)

46.

Solve the equation for x.

a)

7.389

b)

0.693

c)

0.0183

d)

6.581

47.

Rewrite the equation in logarithmic form.
$6^2=36$

a)

$\log_636=2$

b)

$\log_236=6$

c)

$\log_{36}6=2$

d)

$\log_62=36$

48.

Rewrite the equation in logarithmic form.
$12^0=1$

a)

$\log_012=1$

b)

$\log_{12}0=1$

c)

$\log_{12}1=0$

d)

$\log_112=0$

49.

Rewrite the equation in logarithmic form.

a)

$\log_{\frac{1}{16}}16=-1$

b)

$\log_{16}\left(\frac{1}{16}\right)=-1$

c)

$\log_{-1}\left(\frac{1}{16}\right)=16$

d)

$\log_{\frac{1}{16}}-1=16$

50.

Logarithms are the inverse of ___________.

a)

Trees

b)

Quadratics

c)

Square

d)

Exponential

51.

Expand the Log completely and simplify if possible. $\log_{ }\left(\frac{\sqrt{x}}{z^5y}\right)$

a)

$\frac{1}{2}\log x\ -5\log z-\log y$

b)

$\log\ x^{\frac{1}{2}\ }-\log\ z^5+\log\ y$

c)

$\log\ \sqrt{x}-\log z^5+y^{ }$

d)

$10\log\ x-z+y$

52.

a)

A

b)

B

c)

C

d)

D

53.

a)

A

b)

B

c)

C

d)

D

54.

a)

6log₈(xyz)

b)

log₈(x) - log₈(y) - 6log₈(z)

c)

log₈(x) + log₈(y) - log₈(z)

d)

log₈(x) + log₈(y) + 6log₈(z)

55.

Expand the logarithm expression

log 6x³y

a)

log 6x³ + log y

b)

log 6 + log x³ + log y

c)

3 log 6 + log x + log y

d)

log 6 + 3log x + log y

56.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

57.

Change to Logarithmic Form:
5³ = 125

a)

log ₅ 125 = 3

b)

log₃125 = 5

c)

log ₅ 3 =125

d)

log₁₂₅ 3 = 5

58.

Condense to a single logarithm.

a)

ln x⁴/ y

b)

ln xy⁴

c)

ln x/ y⁴

d)

ln x⁴/ y⁴

59.

Condense.

a)

log₂x²y¹⁰

b)

log₂x²+log₂y¹⁰

c)

log₂x²/y¹⁰

d)

log₂10xy

60.

Expand.

a)

log x + 5 log y

b)

5 log x + 5 log y

c)

5 log x - log y

d)

log x - 5 log y

61.

Condense

a)

logxyz³

b)

log(xy/z³)

c)

logx+logy+logz³

d)

logx³y³z³

62.

Expand

a)

6log₈v-2log₈u

b)

6log₈u-2log₈v

c)

3log₈u-2log₈v

d)

6log₈u+2log₈v

63.

Riley invested $1,000 in savings bonds. If the bonds earn 6.75% interest compounded semi-annually, how much total will Riley earn in 15 years?

a)

$1,584.62

b)

$2,651.39

c)

$2,706.86

d)

$1,825.10

64.

Olivia would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.

a)

$15,415.94

b)

$15,683.28

c)

$15,927.56

d)

$16,109.05

65.

Approximately what interest rate would be needed in order to grow an investment of $1,400 to $2,500 in 10 years if the interest was compound monthly?

a)

5.96%

b)

5.84%

c)

5.81%

d)

5.88%

66.

If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

a)

$1,225,54

b)

$2,225.54

c)

$22,255.40

d)

$225.54

67.

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

a)

A

b)

B

c)

C

d)

D

68.

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

a)

A

b)

B

c)

C

d)

D

69.

Rewrite in exponential form.

a)

A

b)

B

c)

C

d)

D

70.

Solve the equation.

a)

A

b)

B

c)

C

d)

D

71.

log₂(x + 5) = 3

a)

3

b)

4

c)

5

d)

6

72.

Solve:
_{log (4x − 5) = log (2x − 1)}

a)

0

b)

1

c)

2

d)

3

73.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?

a)

y=8(15,000)^x

b)

y=15,000(1.08)^x

c)

y=15,000(0.92)^x

d)

y=15,000(0.08)^x

74.

What would the change base look like for:
log₆ 48

a)

log 8

b)

^{log 6}/_{log 48}

c)

^{log 48}/_{log 6}

d)

ln 8

75.

In an exponential function, what does the 'a' represent?

a)

SLOPE

b)

RATE OF CHANGE

c)

STARTING VALUE
(y-intercept)

d)

GROWTH FACTOR

76.

In an exponential function, what does the 'b' represent?

a)

SLOPE

b)

GROWTH FACTOR

c)

Y-INTERCEPT

d)

STARTING VALUE

77.

The inverse of a logarithmic function and the logarithmic function do what on a graph?

a)

The are perpendicular

b)

They are paralell

c)

They reflect over the line y=x.

d)

There is nothing special .

78.

Write log₂ 0.25 = -2 in exponential form

a)

-2²= 0.25

b)

-2^0.25= 2

c)

2^-2= 0.25

d)

No correct answer

79.

Which of the following represent the a change of base for log_x y using the natural log?

a)

ln x / ln y

b)

ln y / ln x

c)

log x / log y

d)

log y / log x

80.

Expand.

a)

1/3 log x + log y + log z

b)

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

c)

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

d)

3 log x + 3 log y + 3 log z

81.

Solve log(x) + log(x+3) = 1

a)

5

b)

-2

c)

-5

d)

2

82.

log₂(x + 2) + log₂x = 3

a)

-4, 2

b)

-2, 4

c)

2

d)

1

83.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

84.

Solve

a)

A

b)

B

c)

C

d)

D

85.

a)

5

b)

13

c)

84

d)

-20

86.

a)

no solution

b)

only 6

c)

6 and -2

d)

3

87.

log₄(3x-1)=log₄(2x+3)

a)

4

b)

3

c)

1

d)

8

88.

log₂(x²- 6) = log₂(2x+2)

a)

4, -2

b)

No Solution

c)

4

d)

-2

89.

log₂(x+3)=4

a)

16

b)

13

c)

3

d)

10

90.

log_x1000=3

a)

1

b)

10

c)

30

d)

3

91.

log₈(4x+4)=2

a)

15

b)

12

c)

10

d)

3

92.

a)

x is undefined

b)

x = 2

c)

x= 0.4

d)

x = 33

93.

a)

x = 5 and x = -2

b)

x = -2

c)

x = 5

d)

x = -10 and x = 10

94.

a)

x = 21

b)

x= 49/3

c)

x = 49

d)

x = 147

95.

Log with a base "e" (log_e) is the same thing as...

a)

"e"

b)

Natural Logarithm (LN)

c)

Common Logarithm (Log)

d)

Natural Log, base "e"
LN_e

Unit 7 Review

Total questions: 95

Worksheet time: 18hrs 32mins

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