Question

The value of $lo{g}_{\sqrt{\sqrt{2}}}\cdot \sqrt{2\sqrt{2\sqrt{2\sqrt{2\sqrt{2}}}}}$ is .....

• A. $\frac{31}{32}$
• B. $\frac{31}{4}$
• C. $\frac{31}{8}$
• D. None

Answer 1

The correct option is C $\frac{31}{8}$

$Usingthehintthegivenexpressioncanbewrittenas{\log }_{2^{\frac{1}{4}}}{(2}^{(1-\frac{1}{2^5})}\left)Let{\log }_{2^{\frac{1}{4}}}{(2}^{(1-\frac{1}{2^5})}\right)=x{2}^{(1-\frac{1}{2^5})}={(2}^{\frac{1}{4}}{)}^x{2}^{\frac{31}{32}}=2^{\frac{x}{4}}So\frac{31}{32}=\frac{x}{4}Sox=\frac{31}{8}$