The logarithms require x>0 and x³>3. Combine the right side: \[3\ln x-\ln3=\ln(x^3/3).\] Since the logarithm is one-to-one, \[x^3-3=x^3/3,\qquad2x^3=9,\qquad x=\sqrt[3]{9/2}.\] This satisfies the domain. To 3 significant figures, \[\boxed{x=1.65}.\]