A) \[\sqrt{y}\]
B) \[y\]
C) \[{{y}^{2}}\]
D) \[{{y}^{4}}\]
Correct Answer: C
Solution :
Given \[y={{2}^{1/{{\log }_{x}}4}}\Rightarrow \log y=\frac{1}{{{\log }_{x}}4}(\log 2)\] \[\Rightarrow {{\log }_{x}}4=\frac{\log 2}{\log y}\Rightarrow \frac{{{\log }_{e}}4}{{{\log }_{e}}x}=\frac{{{\log }_{e}}2}{{{\log }_{e}}y}\Rightarrow \frac{2\log 2}{\log x}=\frac{\log 2}{\log y}\] Þ \[2\log y=\log x\Rightarrow x={{y}^{2}}\].
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