Answer:
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\\====================================[/tex]
[tex]10-2\log_9\left(\dfrac{1}{4}x\right)=9\qquad\text{subtract 10 from both sides}\\\\-2\log_9\left(\dfrac{1}{4}x\right)=-1\qquad\text{divide both sides by (-2)}\\\\\log_9\left(\dfrac{1}{4}x\right)=\dfrac{1}{2}\iff\dfrac{1}{4}x=9^\frac{1}{2}\\\\\dfrac{1}{4}x=\sqrt9\\\\\dfrac{1}{4}x=3\qquad\text{multiply both sides by 4}\\\\x=12\in D[/tex]
