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Question Number 157770 by Oberon last updated on 27/Oct/21

Can you proof this intresting identity?  ln x = (x−1)Π_(n=1) ^∞  ((2/(1+(x)^(1/2^n ) )))

$$\mathrm{Can}\:\mathrm{you}\:\mathrm{proof}\:\mathrm{this}\:\mathrm{intresting}\:\mathrm{identity}? \\ $$$$\mathrm{ln}\:\mathrm{x}\:=\:\left(\mathrm{x}−\mathrm{1}\right)\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\prod}}\:\left(\frac{\mathrm{2}}{\mathrm{1}+\sqrt[{\mathrm{2}^{\mathrm{n}} }]{\mathrm{x}}}\right) \\ $$

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