Logarithm and Antilogarithm Test 7

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Logarithm and Antilogarithm Test 7

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Weekly Quiz Competition

Question 1
1 / -0

The value of $$21^{0}$$ is _____.

A
$$0$$

B
$$21$$

C
$$1$$

D
$$-21$$

Solution

$$21^{0} = 1$$
$$\because a^{0} = 1$$
This is the law for zero exponent.
So, option $$C$$ is correct.
Question 2
1 / -0

The value of $$((6)^{0} + (16)^{0}) \div ((7)^{0} + (17)^{0})$$ is _____

A
$$2$$

B
$$4$$

C
$$1$$

D
$$0$$

Solution

$$((6)^{0} + (16)^{0}) \div ((7)^{0} + (17)^{0})$$
$$ = (1 + 1)\div (1 + 1)$$
$$= 2\div 2$$
$$= 1$$
So, option $$C$$ is correct.
Question 3
1 / -0

The value of $$(100)^{0}$$ is _____.

A
$$1$$

B
$$0$$

C
$$100$$

D
$$1000$$

Solution

According to the law of power of $$0$$,
$$(100)^{0} = 1$$.

So, option $$A$$ is correct.
Question 4
1 / -0

Evaluate: $$({(10)^0} + (12)^{0})\times (18)^{0}$$

A
$$1$$

B
$$0$$

C
$$2$$

D
$$18$$

Solution

$$((10)^{0} + (12)^{0})\times (18)^{0} = (1 + 1) \times 1$$
$$= (2)\times 1$$
$$= 2$$
So. option $$C$$ is correct.
Question 5
1 / -0

What is the value of $$[\log_{10} (5\log_{10} 100)]^{2}$$?

A
$$4$$

B
$$3$$

C
$$2$$

D
$$1$$

Solution

The value of $$[\log_{10}(5\log_{10} 100)]^{2}$$ is
$$=[\log_{10}(5\log_{10}10^2)]^2$$
$$=[\log_{10}(10\log_{10}10)]^2$$ .....As $$\log a^m=m\log a$$
$$=[\log_{10}(10\times 1)]^2$$ ....As $$\log_aa=1$$
$$=[\log_{10}10]^2$$
$$=[1]^2=1$$
Question 6
1 / -0

Given that $$2^h\times 2^3 = 2^9$$, find the value of h.

A
$$3$$

B
$$6$$

C
$$8$$

D
$$12$$

Solution

$$2^{h}\times 2^{3}=2^{9}$$
$$\Rightarrow 2^{h+3}=2^{9}$$
$$\Rightarrow h+3=9$$
$$\Rightarrow \boxed{h=6}$$
Question 7
1 / -0

The value of $$\dfrac{8^5.9^4}{2^{12}.3^6}$$ is

A
48

B
54

C
1152

D
128

E
72

Solution

The value of $$\dfrac { { 8 }^{ 5 }{ 9 }^{ 4 } }{ { 2 }^{ 12 }{ 3 }^{ 6 } } $$
$$=\dfrac { { 2 }^{ 15 }{ 3 }^{ 8 } }{ { 2 }^{ 12 }{ 3 }^{ 6 } } $$
$$={ 2 }^{ (15-12) }{ 3 }^{ (8-6) }$$
$$={ 2 }^{ 3 }{ 3 }^{ 2 }$$
$$=72$$
Question 8
1 / -0

Find the correct expression, if $$\log _{ c }{ a } =x$$.

A
$${ x }^{ c }=a$$

B
$${ a }^{ x }=c$$

C
$${ c }^{ a }=x$$

D
$${ c }^{ x }=a$$

E
None of these

Solution

Given, $$\log _c a=x$$
Taking antilog, we get
$$c^x = a$$.
Question 9
1 / -0

Which one of the following is the value of $$(101)^{0}$$?

A
$$0$$

B
$$101$$

C
$$1010$$

D
$$1$$

Solution

$$101^{0} = 1$$

So, option $$D$$ is correct.
Question 10
1 / -0

The value of $$x$$ satisfying $$\log _{ 243 }{ x } =0.8$$

A
$$81$$

B
$$1.8$$

C
$$2.43$$

D
$$27$$

Solution

$$\log_{243}x=0.8$$
$$\Rightarrow x=243^{0.8}$$
$$\Rightarrow x=81$$
Hence, A is the correct option.

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Re-Attempt Weekly Quiz Competition

Logarithm and Antilogarithm Test 7

Result

Logarithm and Antilogarithm Test 7

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SHARING IS CARING

Question 1

$$0$$

$$21$$

$$1$$

$$-21$$

Solution

Question 2

$$2$$

$$4$$

$$1$$

$$0$$

Solution

Question 3

$$1$$

$$0$$

$$100$$

$$1000$$

Solution

Question 4

$$1$$

$$0$$

$$2$$

$$18$$

Solution

Question 5

$$4$$

$$3$$

$$2$$

$$1$$

Solution

Question 6

$$3$$

$$6$$

$$8$$

$$12$$

Solution

Question 7

48

54

1152

128

72

Solution

Question 8

$${ x }^{ c }=a$$

$${ a }^{ x }=c$$

$${ c }^{ a }=x$$

$${ c }^{ x }=a$$

None of these

Solution

Question 9

$$0$$

$$101$$

$$1010$$

$$1$$

Solution

Question 10

$$81$$

$$1.8$$

$$2.43$$

$$27$$

Solution

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