Logarithm and Antilogarithm Test 3

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Logarithm and Antilogarithm Test 3

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Weekly Quiz Competition

Question 1
1 / -0

The value of $$(\sqrt 8)^{\tfrac 13}$$ is

A
$$2$$

B
$$4$$

C
$$\sqrt 2$$

D
$$8$$

Solution

$$(\sqrt 8)^{\tfrac 13} = (8^{\tfrac 12})^{\tfrac 13}$$ $$ = 8^{ ( \tfrac {1}{2} \times \tfrac {1}{3} )} = 8^{\tfrac {1}{6}}$$

$$\Rightarrow (2^3)^{\tfrac 16} = 2^{(3\times \tfrac {1}{6})} = 2^{\tfrac {1}{2}} = \sqrt 2$$
Question 2
1 / -0

Simplify $$(32)^{\displaystyle \frac {-2}{5}}\, \div\, (125)^{\displaystyle \frac {-2}{3}}$$

A
$$\displaystyle \frac {4}{25}$$

B
$$\displaystyle \frac {25}{4}$$

C
$$\displaystyle \frac {2}{5}$$

D
$$\displaystyle \frac {5}{2}$$

Solution

$$ \cfrac {(32)^{ \tfrac {-2}{5}}}{(125)^{ \tfrac {-2}{3}}} = \cfrac { \cfrac {1}{4}}{ \cfrac {1}{25}} = \cfrac {25}{4}$$
Question 3
1 / -0

If x = 2, y = 3 then $$\displaystyle \frac {1}{x^y}\, +\, \displaystyle \frac {1}{y^x}$$ = .........

A
72

B
$$\displaystyle \frac {17}{72}$$

C
$$\displaystyle \frac {31}{108}$$

D
None of these

Solution

$$\displaystyle \frac {1}{2^3}\, +\, \displaystyle \frac {1}{3^2}\, =\, \displaystyle \frac {1}{8}\, +\, \displaystyle \frac {1}{9}\, =\, \displaystyle \frac {9+8}{72}\, =\, \displaystyle \frac {17}{72}$$
Question 4
1 / -0

$$\left ( \displaystyle \frac {16}{81} \right )^{\displaystyle \frac {3}{4}}$$ = ..........

A
$$\displaystyle \frac {9}{2}$$

B
$$\displaystyle \frac {2}{9}$$

C
$$\displaystyle \frac {8}{27}$$

D
$$\displaystyle \frac {27}{8}$$

Solution

$$\left ( \cfrac {16}{81} \right )^{ \tfrac {3}{4}} = \left [ \left ( \cfrac {2}{3} \right )^4 \right ]^{\tfrac {3}{4}} = \cfrac {8}{27}$$
Question 5
1 / -0

The value of $$(3^{0} - 4^{0})\, \times\, 5^2$$ is

A
$$25$$

B
$$0$$

C

$$-25$$

D
none of these

Solution

To find the value of $$(3^{0} - 4^{0})\, \times\, 5^2$$

$$(3^{0} - 4^{0}) \times 5^2$$
$$ = (1 - 1) \times 25 $$
$$= 0\times25$$
$$= 0$$

Hence, the value is $$0$$
Question 6
1 / -0

The value of $$[ (-2)^{(-2)} ]^{(-3)}$$ is

A
64

B
32

C
cannot be determined

D
none of these

Solution

$$[ (-2)^{(-2)} ]^{(-3)}\, =\, (-2)^6\, =\, 64$$
Question 7
1 / -0

$$(64)^{\displaystyle \frac {-2}{3}}\, \times \left ( \displaystyle \frac {1}{4} \right )^{-3}$$ equals to

A
4

B
$$\displaystyle \frac {1}{4}$$

C
1

D
16

Solution

$$(64)^{ -\tfrac {2}{3}} \times \left ( \cfrac {1}{4} \right )^{-3} = (4^3)^{ -\tfrac {2}{3}} \times \left ( \cfrac {1}{4} \right )^{-3}$$

$$\Rightarrow 4^{-2} \times \cfrac {1}{4^{-3}} $$

$$\Rightarrow 4^{-2+3} = 4^1 = 4$$
Question 8
1 / -0

The value of $$\left ( \displaystyle \frac {-1}{216} \right )^{-2/3}$$ is

A
$$36$$

B
$$-36$$

C
$$\dfrac {1}{36}$$

D
$$-\dfrac{1}{36}$$

Solution

$$\left (\cfrac {-1}{216} \right )^{-\tfrac 23} = \left [ \left (\cfrac {-1}{6} \right )^3 \right ]^{-\tfrac23} $$
$$=\left ( \cfrac {-1}{6} \right )^{3 \times -\tfrac {2}{3}}$$
$$=\left (- \cfrac {1}{6} \right )^{-2} $$
$$= \cfrac {1}{(-1/6)^2} $$
$$= \cfrac {1}{(1/36)} = 36$$
Question 9
1 / -0

The value of $$(256)^{\dfrac 54}$$ is

A
$$512$$

B
$$984$$

C
$$1024$$

D
$$1032$$

Solution

$$(256)^{\dfrac 54} = (4^4)^{\dfrac 54}$$

$$ = 4^{(4\times \dfrac {5}{4})}$$

$$= 4^5 = 1024$$
Question 10
1 / -0

Which of the following values are equal?
I. $$1^4$$
II. $$4^0$$
III. $$0^4$$
IV. $$4^1$$

A
I and II

B
II and III

C
I and III

D
I and IV

Solution

I $$1^4 = 1$$
II: $$4^0 = 1$$
III: $$0^4 = 0$$
IV: $$4^1 = 4$$

Hence, $$1^4=4^0 = 1$$

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Logarithm and Antilogarithm Test 3

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Logarithm and Antilogarithm Test 3

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Question 1

$$2$$

$$4$$

$$\sqrt 2$$

$$8$$

Solution

Question 2

$$\displaystyle \frac {4}{25}$$

$$\displaystyle \frac {25}{4}$$

$$\displaystyle \frac {2}{5}$$

$$\displaystyle \frac {5}{2}$$

Solution

Question 3

72

$$\displaystyle \frac {17}{72}$$

$$\displaystyle \frac {31}{108}$$

None of these

Solution

Question 4

$$\displaystyle \frac {9}{2}$$

$$\displaystyle \frac {2}{9}$$

$$\displaystyle \frac {8}{27}$$

$$\displaystyle \frac {27}{8}$$

Solution

Question 5

$$25$$

$$0$$

$$-25$$

none of these

Solution

Question 6

64

32

cannot be determined

none of these

Solution

Question 7

4

$$\displaystyle \frac {1}{4}$$

1

16

Solution

Question 8

$$36$$

$$-36$$

$$\dfrac {1}{36}$$

$$-\dfrac{1}{36}$$

Solution

Question 9

$$512$$

$$984$$

$$1024$$

$$1032$$

Solution

Question 10

I and II

II and III

I and III

I and IV

Solution

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