Question

( left(1+2 log _{2} xright) cdotleft(4+log _{2} xright)=frac{9}{2}left(log _{2} xright)^{2} )
cel ( log _{2} x=t )
( Rightarrow 2(1+2 t)(4+t)=9 t^{2} )
( Rightarrow 2left(4+9 t+2 t^{2}right)=9 t^{2} )
( Rightarrow quad 5 t^{2}-18 t-8=0 )
( 5 t^{2}-20 t+2 t-8=0 )
( Rightarrow(5 t+2)(t-4)=0 )
( Rightarrow quad t=-frac{2}{5}, 4 )
Give rating
( log _{2} x=-frac{2}{5}, 4 quad frac{text { palved byon }}{11 text { Tian }} )
( Rightarrow x=2^{-frac{2}{5}} ) ar ( 2^{4} )
( =frac{1}{4^{1 / 5}} ) on 16 thes

# (log 24?) (bag 164) = q (borg, 2)?

Solution