Question

Solve the equation
7-2log3(1/4x)=11

Answer 1

`\large\boxed{x=(4)/(9)}`

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\\\\a^(-n)=(1)/(a^n)\\=======================\\\\7-2\log_3\left((1)/(4)x\right)=11\qquad\text{subtract 7 from both sides}\\\\-2\log_3\left((1)/(4)x\right)=4\qquad\text{divide both sides by (-2)}\\\\\log_3\left((1)/(4)x\right)=-2\iff(1)/(4)x=3^(-2)\\\\(1)/(4)x=(1)/(3^2)\\\\(1)/(4)x=(1)/(9)\qquad\text{multiply both sides by 4}\\\\x=(4)/(9)\in D`