Question

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

• A. 5
• B. 16
• C. 25
• D. 32

Answer 1

Answer: (C)

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