Question

If $\sqrt{{\log }_{2}x}-0.5={\log }_2\sqrt{x}$, then x equals:

• A. Odd integer
• B. Prime number
• C. Composite number
• D. Irrational number

Answer 1

The correct option is B Prime number

$\sqrt{{\log }_{2}x}-0.5={\log }_2\sqrt{x}$

$\Rightarrow \sqrt{{\log }_{2}x}-0.5=0.5{\log }_{2}x$

$\Rightarrow y-0.5=0.5y^2$

$\Rightarrow y^2-2y+1=0$

$\Rightarrow y=1$

$\Rightarrow {\log }_{2}x=1$

$\Rightarrow x=2$