solve in R log equation

$\large \left(\sqrt{|\ln x|+1} +\sqrt{|\ln x|}\right)^{\ln x} + \left(\sqrt{|\ln x|+1} -\sqrt{|\ln x|}\right)^{\ln x} = 2\sqrt 2$

There are 2 solutions to the equation above, $x = a$ and $x=b$ . If $a<b$ , find $a$ to 3 decimal places.

Notation: $|\cdot|$ denotes the absolute value function .