Answer
$x=-3$
Work Step by Step
Use the definition of the log function to solve for $x$. Rewrite the problem so that the base has the exponent of the opposite side and is equal to the log's number and/or variable. Then simplify the side with $x$ by factoring and then solving for $x$. $-7$ is not part of the domain, so $-3$ is the only answer.
$\log_3(x+6)+\log_3(x+4)=1$
$\log_3(x+6)(x+4)=1$
$3^1=x^2+10x+24$
$x^2=10x+21=0$
$(x+7)(x+3)=0$
$x=-7, x=-3$
$x=-3$
