Answer
$x=3$
Work Step by Step
$\log_{3}x+\log_{3}(x+6)=3$
Combine $\log_{3}x+\log_{3}(x+6)$ as the $\log$ of a product:
$\log_{3}x(x+6)=3$
$\log_{3}(x^{2}+6x)=3$
Rewrite in exponential form:
$3^{3}=x^{2}+6x$
$x^{2}+6x=27$
$x^{2}+6x-27=0$
Solve this equation by factoring:
$(x+9)(x-3)=0$
Set both factors equal to $0$ and solve each individual equation for $x$:
$x+9=0$
$x=-9$
$x-3=0$
$x=3$
The initial equation is undefined for $x=-9$, so the answer is just $x=3$
