Question-155510

Question Number 155510 by VIDDD last updated on 01/Oct/21

Answered by puissant last updated on 04/Oct/21

I = \sqrt{{l o g}_{\sqrt{2}} \sqrt{\sqrt{2} \times 2^{\frac{1}{4}}} + {l o g}_{\sqrt[4]{2}} \sqrt[4]{2^{\frac{3}{4}}}}

\Rightarrow I = \sqrt{{l o g}_{\sqrt{2}} 2^{\frac{3}{8}} + {l o g}_{\sqrt[4]{2}} 2^{\frac{3}{16}}}

\Rightarrow I = \sqrt{\frac{\frac{3}{8} l n 2}{\frac{1}{2} l n 2} + \frac{\frac{3}{16} l n 2}{\frac{1}{4} l n 2}}

\Rightarrow I = \sqrt{\frac{3}{4} + \frac{3}{4}} = \sqrt{\frac{6}{4}} = \sqrt{\frac{3}{2}}

∴∵ I = \frac{1}{2} \sqrt{6} \dots

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