Indian Institute of Foreign Trade 2010 Solved Paper

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Question : 14 of 135

Marks: +1, -0

What is the value of

a/√b

, if

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

-5/3
2
5/3
1

Solution:

a/√b

,If

\log_{4}\log_{4}4^{a-b}=2\log_{4}(√{a}-√{b})+\log_{4}4

i.e.

\log_{4}\log_{4}4^{a-b}=\log_{4}((√{a}-√{b})^{2})×4

i.e.

\log_{4}4^{a-b}=((√{a}-√{b})^{2})×4

i.e.

(a-b)×\log_{4}4=((√{a}-√{b})^{2})×4

i.e.

a-b=4a+4b-8√{ab}

i.e.

3a+5b-8√{ab}=0

i.e.

3a/√b^2-8a/√b+5=0

Put

a/√b=t

therefore

3t^2-8t+5=0

solving we get

t=1

or

t=5/3

i.e.

a/√b=1

or

5/3

but if

a/√b=1

then a=b then

\log_4(√a-√b)

will become indefinite
Therefore

a/√b=5/3

Therefore our answer is option 'C'

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