If y = 2^ 1/ _x 4 , then x is equal to - Vidyadip

MCQ

If $y = {2^{1/{{\log }_x}4}}$, then $ x$ is equal to

A
$\sqrt y $
B
$y$
✓
${y^2}$
D
${y^4}$

✓

Answer

Correct option: C.

${y^2}$

c
(c) Given $y = {2^{1/{{\log }_x}4}} \Rightarrow \log y = \frac{1}{{{{\log }_x}4}}(\log 2)$

$ \Rightarrow {\log _x}4 = \frac{{\log 2}}{{\log y}} $

$\Rightarrow \frac{{{{\log }_e}4}}{{{{\log }_e}x}} = \frac{{{{\log }_e}2}}{{{{\log }_e}y}} $

$\Rightarrow \frac{{2\log 2}}{{\log x}} = \frac{{\log 2}}{{\log y}}$

==> $2\log y = \log x \Rightarrow x = {y^2}$.

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