Question

If $y=2^{1/{\log }_{x}4},$ then

• A. $x=y$
• B. $x=y^4$
• C. $x^2=y$
• D. $x=y^2$

Answer 1

The correct option is D $x=y^2$

$y=2^{1/{\log }_{x}4}$
$\Rightarrow {\log }_{2}y=\frac{1}{{\log }_{x}4}(x>0,x\ne 1)$
$\Rightarrow {\log }_{2}y={\log }_{4}x=\frac{1}{2}{\log }_{2}x$
$\Rightarrow 2{\log }_{2}y={\log }_{2}x$
$\Rightarrow {\log }_2{y}^2={\log }_{2}x$
$\Rightarrow y^2=x$