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Q:

$\frac{23 x 12 + 49 x 15}{31^{2} + 50} = ?$

A) 0.5	B) 1
C) 2	D) 3

Answer & Explanation Answer: B) 1

Explanation:

$\frac{276 + 35}{961 + 50} = \frac{1011}{1011} = 1$

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Filed Under: Simplification
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Q:

$2660 o f \frac{1}{7} o f \frac{1}{2} o f \frac{1}{9.5} o f \frac{1}{2} = ?$

A) 1	B) 10
C) 0.1	D) 100

Answer & Explanation Answer: B) 10

Explanation:

$\frac{1}{7} x \frac{1}{2} x \frac{1}{9.5} x \frac{1}{2} x 2660 = \frac{2660}{266} = 10$

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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:

The greatest possible value of n could be $9^{n} < 10^{8}$ if, given that log 3 = 0.4771 and $n \in N$ :

A) 7	B) 8
C) 9	D) 10

Answer & Explanation Answer: B) 8

Explanation:

Taking Log to both sides

we get

n = 8

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Filed Under: Logarithms
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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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Filed Under: Logarithms
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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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Filed Under: Logarithms
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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 a, b, c be the $p^{t h}, q^{t h} a n d r^{t h}$ terms of a GP then the value of (q-r) log a + (r-p) log b + (p-q) log c is :

A) 0	B) 1
C) -1	D) pqr

Answer & Explanation Answer: A) 0

Explanation:

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Filed Under: Logarithms
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