The least value of \( |z| \) where \( z \) is complex number which satisfies the inequality \( \displaystyle \exp\left(\frac{(|z| + 3)(|z| - 1)}{||z| + 1|}\log_e 2\right) \ge \log_{\sqrt{2}}|5\sqrt{7} + 9i|, \, i = \sqrt{-1} \), is equal to:
\( 8 \)
\( 2 \)
\( \sqrt{5} \)
\( 3 \)
