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The least value of |z| where z is complex number which satisfies the inequality

exp $$\bigg(\frac{(|z|+3)(|z|-1)}{\big||z|+1 \big|}log_{e^2}\bigg)$$ $$\geq log_\sqrt{2}\big|5\sqrt{7}+9i \big|,$$

$$i=\sqrt{-1},$$ is equal to:

(1) 3

(2) $$\sqrt{5}$$

(3) 2

(4) 8

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