Answer :

[tex]log6x-3=-4;\ D:6x > 0\to x > 0\to x\in\mathbb{R^+}\\\\log6x=-4+3\\\\log6x=-1\iff10^{-1}=6x\\\\6x=\frac{1}{10}\ \ \ /:6\\\\x=\frac{1}{60}\in D[/tex]