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Q:

The number of solutions of the equation $l o g_{\frac{x}{2}} (x^{2}) + 40 l o g_{4 x} (\sqrt{x}) - 14 l o g_{16 x} (x^{3}) = 0$ is:

A) 0	B) 1
C) 2	D) 3

Answer & Explanation Answer: D) 3

Explanation:

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Filed Under: Logarithms
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Q:

If $\log_{3} (30)$ = $\frac{1}{a}$ and $\log_{5} (30) = \frac{1}{b}$ then the value of $3 \log_{30} (2)$ is:

A) 3(1+a+b)	B) 2(1-a-b)
C) 3(1-a-b)	D) 3(1+a-b)

Answer & Explanation Answer: C) 3(1-a-b)

Explanation:

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Q:

Find x if

$l o g_{\frac{1}{\sqrt{2}}} (\frac{1}{\sqrt{8}}) = l o g_{2} (4^{x} + 1) . l o g_{2} (4^{x + 1} + 4)$

A) 0	B) 1
C) 2	D) None of these

Answer & Explanation Answer: A) 0

Explanation:

By trial and error method, when we substitute

x = 0

Both LHS and RHS are equal.

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Q:

The value of x satisfying the following relation:

$\log_{\frac{1}{2}} (x) = \log_{2} (3 x - 2)$

A) 1/3	B) -1/3
C) 3	D) None of these

Answer & Explanation Answer: D) None of these

Explanation:

But at x=-1/3, log x is not defined.

The only admissible value of x is 1.

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Q:

If $A = \frac{l o g_{3} (2187)}{5}$ and $B = l o g_{243} (2187)$ , then which one of the following is correct?

A) A	B) A=B
C) A>B	D) can't be determined

Answer & Explanation Answer: B) A=B

Explanation:

Given $A = \frac{\log_{3} (2187)}{5} a n d B = \log_{243} (2187)$

$B = \log_{3^{5}} (2187) = \frac{\log_{3} (2187)}{5}$

=> A

Therefore, A = B

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Filed Under: Logarithms
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Q:

If $\frac{\log x}{l + m - 2 n} = \frac{\log y}{m + n - 2 l} = \frac{\log z}{n + l - 2 m}$ , then xyz is equal to

A) 0	B) 1
C) lmn	D) 2

Answer & Explanation Answer: B) 1

Explanation:

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Q:

What is refractive index ?

A) it is defined as the ratio of speed of light in the medium to the speed of light in vacuum.	B) it is defined as the product of speed of light in medium and in vacuum.
C) it is defined as the ratio of speed of light in vacuum to the speed of light in the medium .	D) None of above

Answer & Explanation Answer: C) it is defined as the ratio of speed of light in vacuum to the speed of light in the medium .

Explanation:

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Filed Under: Physics

Q:

Banaue Rice Terraces in Ifugao is located in which country?

A) Burma	B) Brunei
C) Philippines	D) India

Answer & Explanation Answer: C) Philippines

Explanation:

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