Proof of the inequality $(2n/\textrm{log}n -1)/\sqrt{n} \geq \textrm{log} n$ for sufficiently large n?

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I found this inequality in CLRS (Coreman)(Introduction to Algorithms 3rd Edition), on Page - 137 . I can't understand the idea behind the proof.It would be really helpful if someone could provide the proof with proper explanation.