Answer:
[tex]\large\boxed{x=\dfrac{4}{9}}[/tex]
Step-by-step explanation:
[tex]Domain:\dfrac{1}{4}x>0\to x>0\\\\Use\ \log_ab=c\iff a^c=b\ for\ a>0\ \wedge\ a\neq1\ \wedge\ b>0\\\\a^{-n}=\dfrac{1}{a^n}\\=======================\\\\7-2\log_3\left(\dfrac{1}{4}x\right)=11\qquad\text{subtract 7 from both sides}\\\\-2\log_3\left(\dfrac{1}{4}x\right)=4\qquad\text{divide both sides by (-2)}\\\\\log_3\left(\dfrac{1}{4}x\right)=-2\iff\dfrac{1}{4}x=3^{-2}\\\\\dfrac{1}{4}x=\dfrac{1}{3^2}\\\\\dfrac{1}{4}x=\dfrac{1}{9}\qquad\text{multiply both sides by 4}\\\\x=\dfrac{4}{9}\in D[/tex]
