Free Printable Logs

1.

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

a)

$\log4\ +\log5$

b)

$\log\ 20$

c)

$\log4\ -\log5$

2.

Expand the following logarithm:
log₂ 5x.

a)

log₂ 5 - log₂ x

b)

log₂ 5 + log₂ x

c)

2log 5 + 2log x

d)

log5 2 + log_x 2

3.

a)

6log₈(xyz)

b)

log₈(x) - log₈(y) - 6log₈(z)

c)

log₈(x) + log₈(y) - log₈(z)

d)

log₈(x) + log₈(y) + 6log₈(z)

4.

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)

5.

Write as a single log: log 12 + 2 log x

a)

log (12 + 2x)

b)

log (14x)

c)

log (12 * 2x)

d)

log (12x²)

6.

Simplify: 2log(x) + 3log(xy)

a)

log(x⁵y³)

b)

log(5xy)

c)

5log(x²y)

d)

log(6x²y)

7.

Expand

\log_5\left(\frac{12a}{2}\right)

a)

$\log_212a-\log_25$

b)

$\log_512a-\log_52$

c)

$\log_512-\log_5a-\log_52$

d)

$\log_512+\log_5a-\log_52$

8.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

9.

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

a)

log8+logx-logy-logz

b)

log8+logx-logy+logz

c)

log(8x)-log(yz)

d)

8logx-ylogz

10.

Rewrite log_b(xⁿ)

a)

nlog_bx

b)

(log_bx)ⁿ

c)

xⁿlog_bx

d)

log_b(xⁿ)

11.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

12.

a)

log (xy³)

b)

log (x⁶− y³)

c)

log (x⁶/y³)

d)

log (x⁶ + y³)

13.

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)

14.

Write log_b(x/y) as two logs

a)

log_bx-log_by

b)

log_bx+log_by

c)

log_bx*log_by

d)

log_bx/log_by

15.

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

a)

logm-log3-logn

b)

3logm+logn

c)

3logm-logn

d)

3log(m-n)

16.

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

a)

logx+logy

b)

xlogy

c)

log(x-y)

d)

logx-logy

17.

log(xy²)

a)

logx+2logy

b)

logx+logy²

c)

logx-2logy

d)

logx+logy+log2

18.

log(4x)

a)

log4-logx

b)

log4+logx

c)

4logx

d)

xlog4

19.

log(3x)²

a)

2log(3+x)

b)

2log3+logx

c)

log3+2logx

d)

2(log3+logx)

20.

$\ln\left(\frac{2x^2y}{z^4}\right)$

a)

ln2+2lnx+lny+4lnz

b)

ln2+2lnx+lny-4lnz

c)

2ln(2xy)-4lnz

d)

2ln2x+lny-4lnz

21.

$\ln\left(\frac{2x^2y}{z^4}\right)$

a)

ln2+2lnx+lny+4lnz

b)

ln2+2lnx+lny-4lnz

c)

2ln(2xy)-4lnz

d)

2ln2x+lny-4lnz

22.

Write log_b(x/y) as two logs

a)

log_bx-log_by

b)

log_bx+log_by

c)

log_bx*log_by

d)

log_bx/log_by

23.

a)

ln(wvu⁵)

b)

ln(u + v + w⁵)

c)

ln(uvw⁵)

d)

ln(uvw)⁵

24.

Write the expression as a single logarithm. Then simplify if possible.
log₅3 + log₅6 + log₅9

a)

log₅69

b)

log₅56

c)

log₅162

d)

log₅98

25.

Write the expression as a single logarithm. Then simplify if possible.
log 6 - log 3 + 2 log 7

a)

log 98

b)

log 78

c)

log 56

d)

log 45

26.

Expand

a)

A

b)

B

c)

C

d)

D

27.

Condense

a)

A

b)

B

c)

C

d)

D

28.

Write as a single log: log 12 + 2⋅log x

a)

log (12 + 2x)

b)

log (14x)

c)

log (12 * 2x)

d)

log (12x²)

29.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

30.

Using the change of base property, rewrite log₂31

a)

log(2) / log(31)

b)

log(2/31)

c)

log(31)/log(2)

d)

log(31/2)

31.

log₄1 =

a)

0

b)

1

c)

4

d)

DNE

32.

Rewrite log_vn = a in exponential form.

a)

v^a = n

b)

n^a = v

c)

vⁿ = a

d)

aⁿ = v

33.

Condense: log₂6+log₂3=

a)

log₂18

b)

log₂2 = 1

c)

log₂3

d)

log₂9

34.

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

35.

Evaluate log_b(b)

a)

-1

b)

0

c)

1

d)

b

36.

Simplify log₄4^3x

a)

3x

b)

3

c)

4

d)

4^3x

37.

Evaluate log₉(9)

a)

-1

b)

1

c)

0

d)

9

38.

Evaluate
log₃81

a)

4

b)

-4

c)

1

d)

0

39.

Evaluate
log₃(1/9)

a)

2

b)

-2

c)

1

d)

3

40.

a)

log (xy³)

b)

log (x⁶− y³)

c)

log (x⁶/y³)

d)

log (x⁶ + y³)

41.

log₄1 =

a)

0

b)

1

c)

4

d)

DNE

42.

Evaluate log₈ 8

a)

8

b)

-1

c)

0

d)

1

43.

Evaluate log₅125

a)

5

b)

3

c)

125

d)

25

44.

Condense into a single logarithm.
$\ln7-\ln2$

a)

ln 5

b)

ln 14

c)

$\ln\frac{2}{7}$

d)

$\ln\frac{7}{2}$

45.

Condense into a single logarithm.
$\log_25+\log_29+\log_2w$

a)

$\log_2\left(14w\right)$

b)

$\log_2\left(45w\right)$

c)

$\log_2\left(\frac{14}{w}\right)$

d)

$\log_2\left(14+w\right)$

46.

Condense into a single logarithm.
$\log_43+2\log_4x+3\log_4y$

a)

$\log_4\left(3x^2y^3\right)$

b)

$\log_4\left(18xy\right)$

c)

$\log_4\left(3xy\right)$

d)

$\log_4\left(8xy\right)$

47.

Condense into a single logarithm.
$4\log_7x-3\log_7y$

a)

$\log_7\left(x^{12}y^3\right)$

b)

$\log_7\left(12xy\right)$

c)

$\log_7\left(\frac{x^4}{y^3}\right)$

d)

$\log_4\left(\frac{4x}{3y}\right)$

48.

Condense into a single logarithm.
$2\ln m+2\ln p-\ln9$

a)

$\ln\left(\frac{4mp}{9}\right)$

b)

$\ln\left(\frac{m^2p^2}{9}\right)$

c)

$\ln\left(36mp\right)$

d)

$\ln\left(m^2p^2-9\right)$

49.

Condense into a single logarithm.
$2\log_5x+2\log_5z+10\log_5y$

a)

$\log_5\left(14xyz\right)$

b)

$\log_5\left(40xyz\right)$

c)

$\log_5\left(x^2y^{10}z^2\right)$

d)

$\log_5\left(xz^2y^{10}\right)$

50.

Expand into multiple logarithms. $\log\left(a^2b^3\right)$

a)

$\log_3\left(2a\right)+\log_3\left(3b\right)$

b)

$\frac{\log_3\left(2a\right)}{\log_3\left(3b\right)}$

c)

$2\log_3a-3\log_3b$

d)

$2\log_3a+3\log_3b$

51.

Expand into multiple logarithms. $\ln\left(\frac{6}{m^4}\right)$

a)

$\ln6-\ln\left(4m\right)$

b)

$\ln6+\ln\left(4m\right)$

c)

$\ln6-4\ln m$

d)

$\ln6-4\ln\left(\frac{1}{m}\right)$

52.

Expand into multiple logarithms. $\log\left(xyz^3\right)$

a)

$\log x+\log y+3\log z$

b)

$3\log x+3\log y+3\log z$

c)

$\log x-\log y-3\log z$

d)

$\left(\log x\right)\left(\log y\right)\left(3\log z\right)$

53.

Expand into multiple logarithms. $\log_5\frac{a^4b}{c^7}$

a)

$\log_5\left(4a\right)+\log_5b-\log_5\left(7c\right)$

b)

$4\log_5a+\log_5b-7\log_5c$

c)

$\log x-\log y-3\log z$

d)

$\left(\log x\right)\left(\log y\right)\left(3\log z\right)$

54.

Rewrite in exponential form:

log₉x=2

a)

9^x=2

b)

2^x=9

c)

2⁹=x

d)

9²=x

55.

Write 6^x = 8 in log form.

a)

log₆ 8 = x

b)

log₈ 6 = x

c)

log₆ x = 8

d)

log₈ x = 6

56.

Write 5^x =10 in log form

a)

x = log 5

b)

x = log₅10

c)

x = 5 log10

d)

x = 10 log 5

57.

Rewrite log₃t = 5 in exponential form.

a)

5^t=3

b)

log₃5 = log₃t

c)

t⁵=3

d)

3⁵=t

58.

Rewrite log_vn = a in exponential form.

a)

v^a = n

b)

n^a = v

c)

vⁿ = a

d)

aⁿ = v

59.

Write in logarithmic form:

a^b = c

a)

log _a c = b

b)

log _b c = a

c)

log _a b = c

d)

log _b a = c

60.

Change to logarithmic form.

3^h = w

a)

log_w3 = h

b)

log₃w = h

c)

log_h3 = w

d)

log₃h = w

61.

Convert 3^x = 12 to the equivalent log form.

a)

3¹² = x

b)

log_x3 = 12

c)

log₃x = 12

d)

log₃ 12 = x

62.

Change to exponential form.

log_a2 = 5

a)

a²= 5

b)

5² = a

c)

a⁵= 2

d)

2⁵ = a

63.

Logarithms are the inverse of ___________.

a)

Trees

b)

Quadratics

c)

Square

d)

Exponential

64.

Write 3 = 7^x in log form.

a)

log₇ 3 = x

b)

log₃ 7 = x

c)

log₇ x = 3

d)

log₃ x = 7

65.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

66.

Rewrite log₂8 = 3 in exponential form.

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

67.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

68.

Change to Logarithmic Form:
5³ = 125

a)

log ₅ 125 = 3

b)

log₃125 = 5

c)

log ₅ 3 =125

d)

log₁₂₅ 3 = 5

69.

log₁₃169=2

a)

2¹³= 169

b)

13² = 169

c)

169² = 13

d)

13¹⁶⁹ = 2

70.

log_n117 = 11

a)

n¹¹= 117

b)

11ⁿ = 117

c)

117ⁿ = 11

d)

n¹¹⁷ = 11

71.

log_nm= -2

a)

n^-2 = m

b)

m^-2 = n

c)

-2ⁿ = m

d)

mⁿ = -2

72.

14² = 196

a)

log₁₄196 = 2

b)

log₂ 14 = 196

c)

log₂ 196 = 14

d)

log₁₄ 14 = 2

73.

n^m = 156

a)

log_n 156 = m

b)

log_n m = 156

c)

log_m 156 = n

d)

log_n 16 = n

74.

Rewrite the equation into logarithmic form:

6² = 36

a)

log₆ 2 = 36

b)

log₆ 36 = 2

c)

ln 36 = 2

d)

6³⁶ = 2

75.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

76.

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

77.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

78.

Change to Exponential Form:

log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

79.

Rewrite log_vn = a in exponential form.

a)

v^a = n

b)

n^a = v

c)

vⁿ = a

d)

aⁿ = v

80.

rewrite into logarithmic form 10⁴ = 10,000

a)

log 4 = 10,000

b)

log₄ 10,000 = 10

c)

log_10,000 4 = 10

d)

log 10,000 = 4

81.

rewrite into logarithmic form 10⁰ = 1

a)

log 1 = 0

b)

log 0 = 1

c)

log ₀ 10 = 1

d)

log ₀ 1 = 10

82.

Rewrite in log form: $17^0=1$

a)

$\log_{17}0=1$

b)

$\log_{17}1=0$

c)

$\log_117=0$

d)

$\log_01=17$

83.

Write in logarithmic form:
9² = 81

a)

log ₉ 81 = 2

b)

log ₂ 81 = 9

c)

log ₉ 2 = 81

d)

log ₂ 9 = 81

84.

Write in logarithmic form:
4⁵ = 1024

a)

log ₄ 1024 = 5

b)

log ₅ 1024 = 4

c)

log ₄ 5 = 1024

d)

log ₅ 4 = 1024

85.

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

86.

Write in exponential form:
log ₃ 6561 = 8

a)

3⁸ = 6561

b)

8³ = 6561

c)

3⁶⁵⁶¹= 8

d)

8⁶⁵⁶¹ = 3

87.

Write in exponential form:
log ₃₆ 1 = 0

a)

36⁰ = 1

b)

36¹ = 0

c)

1³⁶ = 0

d)

1⁰ = 36

88.

Write in exponential form:

log ₂ 32 = 5

a)

2⁵ = 32

b)

5² = 32

c)

5³² = 2

d)

2³² = 5

89.

Convert to exponential form: $\log_{17}289=2$

a)

$17^2=289$

b)

$289^2=17$

c)

$17^{289}=2$

d)

$2^{17}=289$

90.

Convert to exponential form: $\log_71=0$

a)

$1^0=7$

b)

$7^0=1$

c)

$7^1=0$

d)

$0^7=1$

91.

Convert to exponential form: $\log_55=1$

a)

$1^5=5$

b)

$5^5=1$

c)

$5^1=5$

d)

$5^5=5$

92.

Convert to logarithmic form: $2^9=512$

a)

$\log_9512=2$

b)

$\log_2512=9$

c)

$\log_29=512$

d)

$\log_92=512$

93.

Convert to logarithmic form: $11^0=1$

a)

$\log_01=11$

b)

$\log_011=1$

c)

$\log_{ }11=1$

d)

$\log_{11}1=0$

94.

Convert to logarithmic form: $3^x=27$

a)

$\log_x27=3$

b)

$\log_3x=27$

c)

$\log_327=x$

d)

$\log_{27}x=3$

95.

Rewrite the equation into logarithmic form:

6² = 36

a)

log₆ 2 = 36

b)

log₆ 36 = 2

c)

ln 36 = 2

d)

6³⁶ = 2

96.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

97.

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

98.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

99.

Change to Exponential Form:

log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

100.

Rewrite log_vn = a in exponential form.

a)

v^a = n

b)

n^a = v

c)

vⁿ = a

d)

aⁿ = v

101.

rewrite into logarithmic form 10⁴ = 10,000

a)

log 4 = 10,000

b)

log₄ 10,000 = 10

c)

log_10,000 4 = 10

d)

log 10,000 = 4

102.

rewrite into logarithmic form 10⁰ = 1

a)

log 1 = 0

b)

log 0 = 1

c)

log ₀ 10 = 1

d)

log ₀ 1 = 10

103.

Rewrite in log form: $17^0=1$

a)

$\log_{17}0=1$

b)

$\log_{17}1=0$

c)

$\log_117=0$

d)

$\log_01=17$

104.

Write in logarithmic form:
9² = 81

a)

log ₉ 81 = 2

b)

log ₂ 81 = 9

c)

log ₉ 2 = 81

d)

log ₂ 9 = 81

105.

Write in logarithmic form:
4⁵ = 1024

a)

log ₄ 1024 = 5

b)

log ₅ 1024 = 4

c)

log ₄ 5 = 1024

d)

log ₅ 4 = 1024

106.

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

107.

Write in exponential form:
log ₃ 6561 = 8

a)

3⁸ = 6561

b)

8³ = 6561

c)

3⁶⁵⁶¹= 8

d)

8⁶⁵⁶¹ = 3

108.

Write in exponential form:
log ₃₆ 1 = 0

a)

36⁰ = 1

b)

36¹ = 0

c)

1³⁶ = 0

d)

1⁰ = 36

109.

Write in exponential form:

log ₂ 32 = 5

a)

2⁵ = 32

b)

5² = 32

c)

5³² = 2

d)

2³² = 5

110.

Convert to exponential form: $\log_{17}289=2$

a)

$17^2=289$

b)

$289^2=17$

c)

$17^{289}=2$

d)

$2^{17}=289$

111.

Convert to exponential form: $\log_71=0$

a)

$1^0=7$

b)

$7^0=1$

c)

$7^1=0$

d)

$0^7=1$

112.

Convert to exponential form: $\log_55=1$

a)

$1^5=5$

b)

$5^5=1$

c)

$5^1=5$

d)

$5^5=5$

113.

Convert to logarithmic form: $2^9=512$

a)

$\log_9512=2$

b)

$\log_2512=9$

c)

$\log_29=512$

d)

$\log_92=512$

114.

Convert to logarithmic form: $11^0=1$

a)

$\log_01=11$

b)

$\log_011=1$

c)

$\log_{ }11=1$

d)

$\log_{11}1=0$

115.

Convert to logarithmic form: $3^x=27$

a)

$\log_x27=3$

b)

$\log_3x=27$

c)

$\log_327=x$

d)

$\log_{27}x=3$

Logs

Total questions: 115

Worksheet time: 6hrs 49mins

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