Question

# ( log _{1 / 2}^{2}(4 x)+log _{2}left(frac{x^{2}}{8}right)=8 )

Solution

( quad log _{frac{1}{2}}^{2}(4 x)+log _{2}left(frac{x^{2}}{8}right)=8 )

( Rightarrow log _{2}^{2}(4 x)+log _{2}left(frac{x^{2}}{8}right)=8 quad ) 约

( Rightarrowleft(2+log _{2} xright)^{2}+2 log _{2} x-3=8 )

( Rightarrow 4+log _{2}^{2} x+4 log _{2} x+2 log _{2} x=811 )

( Rightarrow quad log _{2} 2 x+6 log _{2} x-7=0 Rightarrowleft(log _{2} x+7right)left(log _{2} x-1right)=0 )

( Rightarrow log _{2} x=1,-7 Rightarrow x=2, frac{1}{128} )