Free Printable LOGARITHMS

1.

If log₅y – log₅√y = 2 log_y 5, then find the value of y.

a)

25

b)

35

c)

10

d)

15

2.

The value of

\frac{1}{\log_360}+\frac{1}{\log_460}+\frac{1}{\log_560}

is

a)

0

b)

1

c)

5

d)

60

3.

If\ \log\frac{a}{b}+\log\frac{b}{a}=\log\left(a+b\right).\ Then

a)

a + b = 1

b)

a - b = 1

c)

a = b

d)

ab=1

4.

If log 27 = 1.431, then the value of log 9 is

a)

0.754

b)

0.854

c)

0.954

d)

0.654

5.

Find the logarithm of 144 to the base $2\sqrt{3}$

a)

2

b)

4

c)

8

d)

None of these

6.

Which of the following statements is not correct?

a)

$\log10$ = 1

b)

$\log\left(2+3\right)=\log\left(2\times3\right)$

c)

$\log1=0$

d)

$\log\left(1+2+3\right)=\log\left(1\times2\times3\right)$

7.

If x, y and z are the sides of a right angled triangle, where ‘z’ is the hypotenuse, then find the value of

$\frac{1}{\log_{\left(x+z\right)}\ y}+\frac{1}{\log_{\left(x-z\right)}\ y}$

a)

1

b)

2

c)

3

d)

4

8.

If ‘x’ is an integer then solve(log₂ x)² – log₂ x⁴ - 32 = 0

a)

125

b)

256

c)

375

d)

None of these

9.

The value of $\log_2\left(\log_5\left(625\right)\right)\ is\ :$

a)

2

b)

5

c)

10

d)

15

10.

$If\ \log_3\left(\log_2x\right)+\left(\log_{\frac{1}{3}}\log_{\frac{1}{2}}y\right)=1\ and\ \ xy^2=4.\ Then\ find\ x+64y.$

a)

1

b)

65

c)

80

d)

100

11.

$\log_2\ x\ +\log_4\ y\ +\log_4\ z\ =\ 2$

\log_3\ y\ +\log_9\ z\ +\log_9\ x\ =\ 2

\log_4\ z\ +\log_{16}\ x\ +\log_{16}\ y\ =\ 2

Then Find the value of

6x+8y+3z

a)

63

b)

56

c)

96

d)

93

12.

$2^x=64$

is equivalent to which of the following?

a)

$\log_x2=64$

b)

$\log_{64}2=x$

c)

$\log_264=x$

d)

$\log_x64=2$

LOGARITHMS

Total questions: 12

Worksheet time: 19mins

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