Question

Solve each equation.
10-2log9(1/4x)=9

Answer 1

x = 12

Explanation:

`Domain:\ (1)/(4)x>0\to x>0\\\\Use:\ \log_ab=c\iff a^c=b\ for\ a>0\ \wedge\ a\\eq1\ \wedge\ b>0\\====================================`

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