Gamma Limit 2

$\underset{x\to \infty }{\text{lim}}\left(\frac{x \Gamma (\log (x)) (\log (x))^{\frac{3}{2}-\log (x)}}{\sqrt{2 \pi }}-\log (x)\right)=\frac{1}{a}$

where $a$ is a positive integer. Submit $a$ .