Differentiation Question 12
Question: If $ y={2^{1/{\log _{x}}4}} $ , then x is equal to
[Roorkee 1998]
Options:
A) $ \sqrt{y} $
B) $ y $
C) $ y^{2} $
D) $ y^{4} $
Show Answer
Answer:
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} $
Therefore $ 2\log y=\log x\Rightarrow x=y^{2} $ .
BETA
