Free Printable LOGS

1.

Select the true equation

a)

$9^{-2}=-81$

b)

$9^{-2}=\frac{1}{18}$

c)

$9^{-2}=\frac{1}{81}$

d)

$9^{-2}=-18$

e)

$9^{-2}=3$

2.

Select the true equation

a)

$12^{\frac{1}{3}}=4$

b)

$12^{\frac{1}{3}}=\sqrt[3]{12}$

c)

$12^{\frac{1}{3}}=\frac{1}{12^3}$

d)

$12^{\frac{1}{3}}=-4$

e)

$2\sqrt[3]{3}$

3.

$r^p=q$ is equivalent to which of the following statements?

a)

$\log_rp=q$

b)

$\log_pq=r$

c)

$\log_qr=p$

d)

$\log_rq=p$

e)

$\log_pr=q$

4.

If $\log_mn=6$ , which of the following statements is always true?

a)

$n=6^m$

b)

$n=m^6$

c)

$m=n^6$

d)

$m=6n$

e)

$n=6$

5.

If $\log_3x=-2$ , then the value of $x$ is

a)

$-6$

b)

$-\frac{3}{2}$

c)

$\frac{2}{3}$

d)

$\frac{1}{6}$

e)

$\frac{1}{9}$

6.

True or false?

$\log_x\left(\frac{1}{x}\right)\ =-1$

a)

TRUE

b)

FALSE

7.

$\log_a\sqrt[]{a}$ is equal to

a)

$\frac{1}{2}$

b)

$\frac{1}{a}$

c)

$-a$

d)

$-2$

e)

undefined

8.

$\log_{25}0.2$ is equal to

a)

$2$

b)

$-2$

c)

$\frac{1}{2}$

d)

$-\frac{1}{2}$

e)

$5$

9.

If $\log_a5=x$ and $\log_a2=y$ , then $\log_a6250$ is equal to?

a)

$x+y$

b)

$5x+y$

c)

$5x+10y$

d)

$4x+10y$

e)

$\left(x+y\right)^2$

10.

$\log_610-\log_62$ is the same as

a)

$\log_68$

b)

$\log_60.2$

c)

$\frac{\log_610}{\log_62}$

d)

$\log_65$

e)

$\log_310$

11.

$2+\log_53$ can be simplified to

a)

$2\log_53$

b)

$\log_{10}3$

c)

$\log_59$

d)

$\log_575$

e)

$\log_5125$

12.

If $\log_b\left(\frac{1}{\sqrt[]{a}}\right)=1.2$ , then $\log_ba$ is equal to?

a)

$-1.44$

b)

$-2.4$

c)

$-0.6$

d)

$\frac{25}{36}$

e)

$-\frac{36}{25}$

13.

$\log_x\left(\frac{1}{\sqrt[]{y}}\right)+\log_x\sqrt[]{y^7}$ is equivalent to

a)

$3\log_xy$

b)

$7$

c)

$6\log_xy$

d)

$\frac{1}{2}\log_xy^7$

e)

$y\log_x7$

14.

True or false?

If $5^{2m}=5^{-\frac{1}{2}}$ , then $2m=-\frac{1}{2}$

a)

TRUE

b)

FALSE

15.

If your calculator only has a "log" button, the solution to $7^x=12$ can be calculated:

a)

$x=\log_{ }\left(\frac{12}{7}\right)$

b)

$x=\log_{ }12-\log_{ }7$

c)

$x=12-\log_{ }7$

d)

$x=\frac{\log_{ }12}{\log_{ }7}$

e)

$x=\log_{ }12^7$

16.

If $\log_23x-\log_25=3$ , then x is

a)

$\frac{40}{3}$

b)

$3$

c)

$\frac{8}{3}$

d)

$1$

e)

$6$

17.

If $\log_3\left(x+2\right)+\log_3\left(x-2\right)=1$ , then $x$ is:

a)

$2$

b)

$\pm2$

c)

$\sqrt[]{7}$

d)

$\pm\sqrt[]{7}$

e)

Undefined

18.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

19.

Write in logarithmic form.
5² = 25

a)

log₅2 = 25

b)

log₂25 = 5

c)

log₂₅5 = 2

d)

log₅25 = 2

20.

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

21.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

22.

Write in exponential form.
log₂(¹/₈) = -3

a)

2^-3 = ¹/₈

b)

2^1/8= -3

c)

-3² = ¹/₈

d)

-3^1/8 = 2

23.

Evaluate:
log₄16

a)

2

b)

4

c)

1/2

d)

-2

24.

Evaluate.
Log₂64

a)

A

b)

B

c)

C

d)

D

25.

log₄1 =

a)

0

b)

1

c)

4

d)

DNE

26.

Solve for x
5^x = 17

a)

x = log₁₇5

b)

x = log 5 + log 17

c)

x = log₅17

d)

x = (log 5)/(log 17)

27.

Solve for x
log₈(x) = 2

a)

x = 256

b)

x = 64

c)

x = 16

d)

x = 32

28.

Solve for x:

a)

1

b)

2

c)

.5

d)

4

29.

log₅(25) = y

a)

y = 2

b)

y = 0.5

c)

y = 5

d)

y = (1/2)

30.

log₃(1) = y

a)

y = 0

b)

y = 1

c)

y = (1/3)

d)

y = 2

31.

log₁₆(4) = y

a)

y = 2

b)

y = 4

c)

y = (1/2)

d)

y = (1/4)

32.

log₂(1/8) = y

a)

y = -3

b)

y = (1/3)

c)

y = 3

d)

y = 0

33.

log₃(4x) = 2

a)

x=4/9
x=4/9

b)

x=9/4

c)

x=3/2

d)

x=2/3

34.

log₂(x + 5) = 3

a)

3

b)

4

c)

5

d)

6

35.

Solve for x:
log₃3^x = 5

a)

5

b)

4

c)

3

d)

243

36.

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

37.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

38.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

39.

Solve for x
5^x = 17

a)

x = log₁₇5

b)

x = log 5 + log 17

c)

x = log₅17

d)

x = (log 5)/(log 17)

40.

Expand

a)

A

b)

B

c)

C

d)

D

41.

Expand

a)

A

b)

B

c)

C

d)

D

42.

Expand

a)

log₈x + log₈y + log₈z

b)

5log₈x + 5log₈y + 5log₈z

c)

log₈xy + 5log₈z

d)

log₈x + log₈y + 5log₈z

43.

Write as a single logarithm:

log(30)-log(6)

a)

-6log(30)

b)

log(24)

c)

log(-24)

d)

log(5)

44.

Rewrite in exponential form:
ln(2) = x

a)

2^x= 10

b)

10² = x

c)

e^x= 2

d)

e² = x

45.

Rewrite e^x = 9 using a logarithm

a)

ln x = 9

b)

ln 9 = x

c)

log_x e = 9

d)

log₉ x = e

46.

Solve for x:
8^x+1= 3

a)

0.528

b)

0.893

c)

-0.472

d)

1.893

47.

Solve the equation for x.

a)

32

b)

25

c)

1.66

d)

512

48.

6^-3x=216

a)

x=3

b)

x=-1

c)

x=6

d)

x=-3

49.

ln(9x-2)=ln(x+14)

a)

x=2

b)

x=.156

c)

x=-3

d)

x=0

50.

Write as one logarithm. Simplify, if possible.
log₃9 + log₃27

a)

-1

b)

5

c)

4

d)

1

51.

Write as one logarithm. Simplify, if possible.
log₂800 - log₂100

a)

8

b)

3

c)

-3

d)

1

52.

Write as one logarithm. Simplify, if possible.
log₅125 - log₅25

a)

1

b)

0

c)

5

d)

-1

53.

Write as one logarithm. Simplify, if possible.
log₆3 + log₆2

a)

0

b)

log₆5

c)

log₆1

d)

1

54.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

55.

Evaluate.
log₆(¹/₂₁₆)

a)

3

b)

¹/₃

c)

-¹/₃

d)

-3

56.

Evaluate.
3 log₂4

a)

3

b)

6

c)

2

d)

4

57.

Evaluate.
3 log₈2

a)

¹/₃

b)

3

c)

1

d)

9

58.

Write in logarithmic form.
5² = 25

a)

log₅2 = 25

b)

log₂25 = 5

c)

log₂₅5 = 2

d)

log₅25 = 2

59.

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

60.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

61.

Write in exponential form.
log₂(¹/₈) = -3

a)

2^-3 = ¹/₈

b)

2^1/8= -3

c)

-3² = ¹/₈

d)

-3^1/8 = 2

62.

Evaluate the following logarithm:

log₃27

a)

3

b)

2

c)

-3

d)

¹/₃

63.

Evaluate the following logarithm:

log₄16

a)

1

b)

-2

c)

2

d)

¹/₂

64.

Evaluate the following logarithm:

log₅5

a)

1

b)

0

c)

-1

d)

¹/₂

65.

Evaluate.
log₆(¹/₂₁₆)

a)

3

b)

¹/₃

c)

-¹/₃

d)

-3

66.

Rewrite log₂8 = 3 in exponential form

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

67.

Rewrite the equation in logarithmic form.

a)

A

b)

B

c)

C

d)

D

68.

Rewrite in exponential form.

a)

A

b)

B

c)

C

d)

D

69.

Evaluate the following logarithm:

log₃27

a)

3

b)

2

c)

-3

d)

¹/₃

70.

Evaluate the following logarithm:

log₅5

a)

1

b)

0

c)

-1

d)

¹/₂

71.

Evaluate the following logarithm:

log₃3

a)

1

b)

0

c)

-1

d)

¹/₂

72.

Evaluate the following logarithm:

log₄16

a)

1

b)

-2

c)

2

d)

¹/₂

73.

Evaluate the following logarithm:

log₄2

a)

-¹/₂

b)

-2

c)

2

d)

¹/₂

74.

Evaluate the following logarithm:

log₈√8

a)

-¹/₂

b)

-1

c)

1

d)

¹/₂

75.

Evaluate the following logarithm:

log₂√2

a)

-¹/₂

b)

-1

c)

1

d)

¹/₂

76.

Evaluate the following logarithm:

log₂₅0.2

a)

-¹/₂

b)

-2

c)

2

d)

¹/₂

77.

Evaluate the following logarithm:

log₄0.5

a)

-¹/₂

b)

-2

c)

2

d)

¹/₂

78.

Evaluate the following logarithm:

log₁₂1

a)

1

b)

0

c)

-1

d)

¹/₂

79.

Evaluate the following logarithm:

log₁₅1

a)

1

b)

0

c)

-1

d)

¹/₂

80.

Evaluate the following logarithm:

log₃(¹/₃)

a)

-2

b)

-¹/₂

c)

-1

d)

¹/₂

81.

Evaluate the following logarithm:

log₄(¹/₆₄)

a)

3

b)

-¹/₃

c)

-3

d)

¹/₃

82.

Evaluate the following logarithm:

log₂₇3

a)

¹/₃

b)

-3

c)

-¹/₂

d)

¹/₂

83.

Evaluate the following logarithm:

log₈4

a)

²/₃

b)

³/₂

c)

³/₄

d)

¹/₂

84.

Evaluate the following logarithm:

log₂₅125

a)

²/₃

b)

³/₂

c)

³/₄

d)

¹/₂

85.

Evaluate the following logarithm:

log₈₁27

a)

²/₃

b)

³/₂

c)

³/₄

d)

⁴/₃

86.

Evaluate the following logarithm:

log₁₆32

a)

⁴/₃

b)

³/₄

c)

⁵/₄

d)

⁴/₅

87.

Evaluate the following logarithm:

log₆36

a)

3

b)

2

c)

1

d)

0

88.

Evaluate the following logarithm:

log₆6

a)

3

b)

2

c)

1

d)

0

89.

$\log_36+\log_32\ =$

a)

$\log_364$

b)

$\log_33$

c)

$\log_312$

d)

$\log_336$

90.

$\log_36-\log_32\ =$

a)

$\log_364$

b)

$\log_33$

c)

$\log_312$

d)

$\log_336$

91.

$2\log_36\ =$

a)

$\log_364$

b)

$\log_33$

c)

$\log_312$

d)

$\log_336$

92.

Logarithmic form of $4^3=64$ is

a)

$\log_43=\ 64$

b)

$\log_34=\ 64$

c)

$\log_{64}4=\ 3$

d)

$\log_464=\ 3$

93.

Evaluate $\log_28$ .

a)

3

b)

4

c)

16

d)

64

94.

$Exponential\ form\ of\ \log_7\ 49=2\ is\$

a)

b)

c)

d)

95.

$\log_axy=$

a)

$\log_ax+\log_ay$

b)

$\log_ax-\log_ay$

c)

$\log_{a\ }x+y$

d)

$m\log_a\ x$

96.

$\log_a\ \left(\frac{x}{y}\right)=$

a)

$\log_ax+\log_ay$

b)

$\log_ax-\log_ay$

c)

$\log_{a\ }x+y$

d)

$m\log_a\ x$

97.

$\log_a\ x^m=$

a)

$\log_ax+\log_ay$

b)

$\log_ax-\log_ay$

c)

$\log_{a\ }x+y$

d)

$m\log_a\ x$

98.

$a^{\log_a\ n}=$

a)

$\log_ax+\log_ay$

b)

$\log_ax-\log_ay$

c)

$n$

d)

$a$

99.

$\log_a\ a\ =$

a)

Not defined

b)

0

c)

1

d)

$a$

100.

$\log_a\ 1\ =$

a)

Not defined

b)

0

c)

1

d)

$a$

101.

$\log_a\ 0\ =$

a)

Not defined

b)

0

c)

1

d)

$a$

102.

$_3^{ }\ \log_36=$

a)

$\log_3216$

b)

6

c)

$\log_312$

d)

$\log_336$

103.

$\log_{10}0.01\ =$

a)

1

b)

2

c)

-1

d)

-2

104.

$\log_{x\ }\sqrt[]{x}\ =$

a)

1

b)

2

c)

$\frac{1}{2}$

d)

x

105.

$\log_{10}\ 1000=$

a)

3

b)

2

c)

-3

d)

-2

106.

$\log_7\ 1\ =$

a)

Not defined

b)

0

c)

1

d)

$a$

107.

$\log_{10}2\ \ is\ \$

a)

Rational number

b)

Irrational number

c)

Integer

d)

Natural number

108.

$\log_{25\ }5\ =$

a)

1

b)

25

c)

$\frac{1}{2}$

d)

5

109.

$\log_216$

a)

8

b)

4

c)

6

110.

$\log_5625$

a)

5

b)

4

c)

25

111.

$\log_5\ \frac{1}{25}$

a)

$\frac{1}{2}$

b)

2

c)

-2

112.

$\log_{\frac{1}{3}}\ 9$

a)

$\frac{1}{3}$

b)

2

c)

-2

113.

$\log_{\frac{1}{3}}\ \frac{1}{9}$

a)

$\frac{1}{3}$

b)

2

c)

-2

114.

$\log_{\frac{1}{4}}\ 16$

a)

$\frac{1}{3}$

b)

2

c)

-2

115.

$\log25\ +\ \log\ 4$

a)

$\frac{1}{3}$

b)

2

c)

-2

116.

$\log_230\ -\ \log_215$

a)

$1$

b)

2

c)

-2

117.

$2^{\log_210}=...\ .$

a)

log 10

b)

log 2

c)

10

118.

Evaluate log_b(b)

a)

-1

b)

0

c)

1

d)

b

119.

Evaluate.
3 log₂4

a)

3

b)

6

c)

2

d)

4

120.

Rewrite in logarithmic form. 7⁰=1

a)

log₀7=1

b)

log₇0=1

c)

log₇1=0

d)

log₁7=0

121.

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

a)

log8+logx-logy-logz

b)

log8+logx-logy+logz

c)

log(8x)-log(yz)

d)

8logx-ylogz

122.

log(3x)²

a)

2log(3+x)

b)

2log3+logx

c)

log3+2logx

d)

2(log3+logx)

123.

ln(4xy)

a)

ln4+lnx+lny

b)

4lnxy

c)

4lnx+lny

d)

4ln(x+y)

124.

$\log\left(\frac{m^3}{n}\right)$

a)

logm-log3-logn

b)

3logm+logn

c)

3logm-logn

d)

3log(m-n)

125.

log(x⁷)

a)

log(7x)

b)

log7+logx

c)

xlog7

d)

7logx

126.

$\log\left(\frac{9}{4}\right)$

a)

log9+log4

b)

log(9-4)

c)

log9-log4

d)

4log9

127.

$\log_4x^2=\log_43+\log_4\left(x+6\right)$

Which quadratic equation would you wind up solving when solving the log equation?

a)

$x^2-3x-18=0$

b)

$x^2+3x+6=0$

c)

$x^2-3x-6=0$

d)

$x^2-x-9=0$

128.

$4\log_2\left(2x+24\right)-17=-9$
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

129.

log₂32=3x

a)

5/3

b)

3/5

c)

5

d)

3

130.

log₄(3x-1)=log₄(2x+3)

a)

4

b)

3

c)

1

d)

8

131.

log_x1000=3

a)

1

b)

10

c)

30

d)

3

132.

log₈(4x+4)=2

a)

15

b)

12

c)

10

d)

3

133.

Solve for x:
4²^x+ 1 = 17

a)

x = 1

b)

x = -1

c)

x = 2

d)

x = -2

134.

log₈(1/2) = x

a)

-1/3

b)

1/3

c)

1/2

d)

-1/2

135.

Solve

\log_5x+\log_x25=3

a)

5

b)

10

c)

25

d)

30

136.

Solve

7\log_x3-\log_3x=6

a)

0

b)

3

c)

$3^{-3}$

d)

$3^{-7}$

137.

Solve the equation.

a)

0

b)

2/3

c)

3/2

d)

1

138.

Solve:
log x + log 8 = 2

a)

10

b)

12.5

c)

15

d)

17.5

139.

Finish solving for x.

Fill in the blank in the box below

(a)

140.

Continue solving for x. Which is the correct "step 2"?

a)

$64=x^3$

b)

$64^3=x$

c)

$x^{64}=3$

d)

$3^{64}=x$

141.

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

a)

$\log\left(64\right)=\log\left(3x\right)$

b)

$\log\left(16\right)=\log\left(x^3\right)$

c)

$\log\left(16\right)=\log\left(3x\right)$

d)

$\log\left(64\right)=\log\left(x^3\right)$

e)

$\log\left(1\right)=\log\left(x^3\right)$

142.

Solve the equation $\log_8\left(-4r-3\right)=\log_8\left(4r+5\right)$

a)

1/3

b)

7

c)

-1

d)

-1/14

143.

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

144.

Solve for x. $\log_52+\log_5x=\log_520$

a)

x = 20

b)

x = 10

c)

x = 2

d)

$x=\frac{1}{10}$

145.

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)

$\log_754=\log_7x$

146.

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: $3^x=3^9$

147.

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

a)

$\log\left(64\right)=\log\left(3x\right)$

b)

$\log\left(16\right)=\log\left(x^3\right)$

c)

$\log\left(16\right)=\log\left(3x\right)$

d)

$\log\left(64\right)=\log\left(x^3\right)$

e)

$\log\left(1\right)=\log\left(x^3\right)$

148.

Which is the correct "step 1" to solve for x?
Hint: look at the schoology discussions if you feel stuck

a)

$\log_2\left(100x^5\right)=7$

b)

$\log_2\left(95x\right)=7$

c)

$\log_2\left(20x\right)=7$

d)

$\log_2\left(500x\right)=7$

149.

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

150.

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

LOGS

Total questions: 150

Worksheet time: 7hrs 45mins

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