Question

Solve the following equation:
${\log }_4(x+3)-{\log }_4(x-1)=2-{\log }_{4}8$

Answer 1

${\log }_4(x+3)-{\log }_4(x-1)=2-{\log }_{4}8\Rightarrow {\log }_4\left(\frac{x+3}{x-1}\right)=2-{\log }_{2^2}{2}^3\Rightarrow {\log }_4\left(\frac{x+3}{x-1}\right)=2-\frac{3}{2}\Rightarrow \frac{x+3}{x-1}=2\Rightarrow x+3=2x-2\Rightarrow x=5.$