Answer
$x=-1$
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 $x$. $-6$ is not part of the domain, so $-1$ is the only answer.
$\log_6(x+3)+\log_6(x+4)=1$
$\log_6(x+3)(x+4)=1$
$6^1=x^2+7x+12$
$x^2+7x+6=0$
$(x+1)(x+6)=0$
$x=-6, x=-1$
$x=-1$
