Question

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

A. 0

B. 1/3

C. 1/2

D. 1

Answer 1

the value of log is 1/2

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

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