The solution set of equation ₓ 2 ₂x} 2 = ₄x} 2is;

Correct Answer is : 2−2,222^{-{2}}, 2^{{2}}2−2,22

Correct Answer is : 2−2,222^{-{2}}, 2^{{2}}2−2,22

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NIMCET 2016 Question Paper with solutions

Question : 52 of 120

Marks: +1, -0

\log_{x}

\log_{2x}

\log_{4x}

2is;

Solution:

\log_{x}2 \log_{2x}2 = \log_{4x}2

\because \log_{x}2

= \frac{1}{\log_{2}x}, \log_{2x}2

= \frac{1}{\log_{2}(2x)}

and

\log_{4x}2 = \frac{1}{\log_{2}(4x)}

\Rightarrow \frac{1}{\log_{2}x} * \frac{1}{\log_{2}(2x)}

= \frac{1}{\log_{2}(4x)}

\Rightarrow \log_{2}x \log_{2}(2x) = \log_{2}(4x)

\Rightarrow \log_{2}x (\log_{2}2 + \log_{2}x)

= \log_{2}4 + \log_{2}x

Let

\log_{2}x

a

\Rightarrow a(1+a)

= \log_{2}2^{2} + a \; (\because \log_{2}2=1)

\Rightarrow a + a^{2} = 2 + a

\Rightarrow a = \pm \sqrt{2}

\Rightarrow \log_{2}x = \pm \sqrt{2}

\Rightarrow x = 2^{\sqrt{2}}, 2^{-\sqrt{2}}

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