Question

Solve the following equations and find the solution:

${\log }_3(x+1)+{\log }_3(x+3)=1$

Answer 1

${\log }_3(x+1)+{\log }_3(x+3)={\log }_3(x+1)(x+3)=1$
$\Rightarrow (x+1)(x+3)=3\Rightarrow x^2+4x=0\Rightarrow x=0,-4.$
Also $x+1>0$ or $x>-1$
and $x+3>0$ or $x>-3$
Hence solutions is $x=0.$