Indian Institute of Foreign Trade 2009 Solved Paper

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Question : 98 of 122

Marks: +1, -0

If

\log_2x.\log{x/64}2=\log{x/16}2

. Then x is

2
4
16
12

Solution:

\log_2x.\log{x/64}=\log{x/16}2

i.e.

{\log x}/{\log2}×{\log2}/{\log x-\log64}={\log2}/{\log x-\log16}

i.e

{\log x×(\log x-\log16)}/{\logx-\log64}=\log2

let

t=\logx

Therefore,

{t×(t-\log16)}/{t-\log64}=\log2

t^{2}-4×\log2×t=t×\log2-6×(\log2)^{2}

i.e.

t^{2}-5×\log2×t-6×(\log2)^{2}=0

i.e.

t^{2}-3×\log 2×t-2×\log2×t-6×(\log2)^{2}=0

i.e.

t×(t-3×\log2)-2×\log2×(t-3×\log2)=0

i.e.

t=2×\log2

or

\;t=3×\log2

i.e.

\log x=\log4

or

\log x=\log8

therefore

x=4

or 8
therefore our answer is option 'B'

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