Answer
$-1$
Work Step by Step
1. $log_6(x+3)+log_6(x+4)=1 \Longrightarrow log_6[(x+3)(x+4)]=log_66 \Longrightarrow x^2+7x+12=6 \Longrightarrow x^2+7x+6=0 \Longrightarrow (x+6)(x+1)=0 \Longrightarrow x=-6,-1 $
2. Check, $x=-1$ fit(s).
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