Answer
$x=2$
Work Step by Step
$\log_{4}x+\log_{4}(x+6)=2$
Combine $\log_{4}x+\log_{4}(x+6)$ as the $\log$ of a product:
$\log_{4}x(x+6)=2$
$\log_{4}(x^{2}+6x)=2$
Rewrite in exponential form:
$4^{2}=x^{2}+6x$
$x^{2}+6x=16$
Take the $16$ to the left side of the equation:
$x^{2}+6x-16=0$
Solve this equation by factoring:
$(x+8)(x-2)=0$
Set both factors equal to $0$ and solve each individual equation for $x$:
$x+8=0$
$x=-8$
$x-2=0$
$x=2$
The initial equation is undefined for $x=-8$, so the answer to this is just $x=2$
