Question

What is the value of log(e(e(e.....)^1/2)^1/2)^1/2)?

Answer 1

$log( \sqrt{e \sqrt{e \sqrt{e \sqrt{e \sqrt{e......} } } } } )$
take
$y = \sqrt{e \sqrt{e \sqrt{e \sqrt{e \sqrt{e.....} } } } }$
then
$y = \sqrt{ey}$
${y}^{2} = ey$
$y = e$
$log(e)$
$1$

Answer 2

Step-by-step explanation:

$\sf \: log( \sqrt{e \sqrt{e \sqrt{e \sqrt{e \sqrt{e......} } } } } )$

take

$\sf \: y = \sqrt{e \sqrt{e \sqrt{e \sqrt{e \sqrt{e.....} } } } } \\ \\ </p><p>$

then

$\sf \: y = \sqrt{ey}</p><p> \\ </p><p> \sf \: {y}^{2} = e</p><p>$