Find all real numbers x which satis...
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Find all real numbers ( x ) which satisfy the equation ( 2 log _{2} log _{2} x+log _{1 / 2} log _{2}(2 sqrt{2} x)=1 )

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Maths
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Find all real numbers x which satisfy the equation 2 log_2 log_2 x + log_1/2 log_2 (2√2–x)=1
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( quad 2 log _{2} log _{2} x+log _{1 / 2} log _{2}(2 sqrt{2} x)=1 )
( Rightarrow 2 log _{2} log _{2} x=log _{2} log _{2}(2 sqrt{2} x)=1 )
( Rightarrow log _{2}left(frac{left.log _{2} xright)^{2}}{log _{2}(2 sqrt{2} x)}=1right. )
( Rightarrow quadleft(log _{2} xright)^{2}=2 log _{2}(2 sqrt{2} x) )
( Rightarrowleft(log _{2} xright)^{2}=log _{2}left(8 x^{2}right) )
( Rightarrowleft(log _{2} xright)^{2}=log _{2} 8+2 log _{2} x )
( Rightarrowleft(log _{2} xright)^{2}-2 log _{2} x-3=0 )
( Rightarrowleft(log _{2} x-3right)left(log _{2} x-1right)=0 )
( Rightarrow log _{2} x=1,3 )
( x=2^{prime}, 2^{3} )
( x=2,8 )

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