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Indian Institute of Foreign Trade 2010 Solved Paper

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Question : 14 of 135

Marks: +1, -0

What is the value of

\frac{a}{\sqrt{b}}

\log_4 \log_4 4^{a-b} = 2 \log_4(\sqrt{a} - \sqrt{b}) + 1

-5/3
2
5/3
1

Solution:

\frac{a}{\sqrt{b}}

,If

\log_4 \log_4 4^{a-b} = 2 \log_4(\sqrt{a} - \sqrt{b}) + \log_4 4

i.e.

\log_4 \log_4 4^{a-b} = \log_4((\sqrt{a} - \sqrt{b})^{2}) \times 4

i.e.

\log_4 4^{a-b} = ((\sqrt{a} - \sqrt{b})^{2}) \times 4

i.e.

(a-b) \times \log_4 4 = ((\sqrt{a} - \sqrt{b})^{2}) \times 4

i.e.

a-b = 4a + 4b - 8\sqrt{ab}

i.e.

3a + 5b - 8\sqrt{ab} = 0

i.e.

\frac{3a}{(\sqrt{b})^{2}} - \frac{8a}{\sqrt{b}} + 5 = 0

Put

\frac{a}{\sqrt{b}} = t

therefore

3t^2 - 8t + 5 = 0

solving we get

t = 1

or

t = \frac{5}{3}

i.e.

\frac{a}{\sqrt{b}} = 1

or

\frac{5}{3}

but if

\frac{a}{\sqrt{b}} = 1

then a=b then

\log_4(\sqrt{a} - \sqrt{b})

will become indefinite

Therefore

\frac{a}{\sqrt{b}} = \frac{5}{3}

Therefore our answer is option 'C'

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