Question

Solve the following equations.
$log(5-x)+log(3-x)=1.$

Answer 1

$\log (5-x)+\log (3-x)=1$

Here, $x<3$

$⟹\log (x^2-8x+15)=1$

$⟹x^2-8x+15=10$

$⟹x^2-8x+5=0$

$⟹x=\frac{8\pm \sqrt{44}}{2}=4\pm \sqrt{11}$

Hence, $x=4-\sqrt{11}$