Answer
$$ D=x \in \mathbb R; x \gt 0~~\text{or}~~ x\lt -3$$
Work Step by Step
The domain of the logarithm function is: $$ D=x \in \mathbb R; x^2+3x \gt 0$$ $$ D=x \in \mathbb R; x(x+3) \gt 0$$ $$ D=x \in \mathbb R; x\gt 0~~\text{and}~~(x+3) \gt 0$$ or$$ D=x \in \mathbb R; x\lt 0~~\text{and}~~(x+3) \lt 0$$
$$ D=x \in \mathbb R; x\gt 0~~\text{and}~~x \gt -3$$ or $$ D=x \in \mathbb R; x\lt 0~~\text{and}~~x \lt -3$$
The intersection gives: $$ D=x \in \mathbb R; x\gt 0$$ or $$ D=x \in \mathbb R; x\lt -3$$
so the domain is:
$$ D=x \in \mathbb R; x \gt 0~~\text{or}~~ x\lt -3$$
