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Q. The value of $x$ satisfying the equation $\sqrt{2} \log _2 2^{\log _2 2^{\log _2 2^{\log _2 2^{\log _2 x}}}}=5$, is

Continuity and Differentiability

Solution:

Using $a ^{\log _{ a } N }= N$ repeatedly, we get $(\sqrt{2})^{\log _2 x}=5 \Rightarrow 2^{\log _2 \sqrt{ x }}=5$
$\Rightarrow \sqrt{ x }=5 \Rightarrow x =25 .$