Big problem, small solution

Algebra Level 4

log2(1+x)=log3x\log _{ 2}{ (1+\sqrt{x})}=\log_{3}{x}

(1+a22a)y(1a22a)y=1,{ (\frac { 1+a^{ 2 } }{ 2a } ) }^{ y }-{( \frac { 1-a^{ 2 } }{ 2a } )}^{ y }=1, 0<a10<a\le1

xy=?\frac { x }{ y } =?

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