The minimum value of x/logx(x≠1) is :

The correct answer is Option (1) → $e$

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

$y'=\frac{-x×\frac{1}{x}+\log x}{(\log x)^2}=\frac{\log x-1}{(\log x)^2}$

for critical points,

$y'(c)=0$

$⇒\log c-1=0$

$⇒\log c=1$

$⇒c=e$

$∴y_{min}=\frac{e}{\log e}=e$