A) \[1/e\]
B) \[e\]
C) \[-1/e\]
D) \[0\]
Correct Answer: A
Solution :
We have,\[f(x)={{\log }_{x}}(\log x)=\frac{\log (\log x)}{\log x}\] \[\Rightarrow \]\[f(x)=\frac{\log x\cdot \frac{1}{\log x}\cdot \frac{1}{x}-\log (\log x)\cdot \frac{1}{x}}{{{(\log x)}^{2}}}\] \[=\frac{1-\log (\log x)}{x{{(\log x)}^{2}}}\] \[\therefore \] \[f(e)=\frac{1-\log (\log e)}{e{{(\log e)}^{2}}}=\frac{1}{e}\]
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