Quick but not simple question. $2^\sqrt2$ or e, which is greater? 
$2^\sqrt2$ vs $e$, which is greater?

$(2^\sqrt2)^\sqrt2 = 4\quad $  &  $\quad e^\sqrt2$ = ?
$\log(2^\sqrt2) = \sqrt2\log(2)\quad$ & $\quad \log(e) = 1$
I tried but can't induce comparable form.
Is anybody know how to prove it?

$2\sqrt{2}^2 = 8$
$e^2 < 2.8*2.8 = 7.84$
You're welcome
