\(D:x\in\mathbb{R^+}\\\\2\ln e^{\ln2x}-\ln e^{\ln10x}=\ln30\\2\ln2x\cdot\ln e-\ln10x\cdot\ln e=\ln30\\2\ln2x-\ln10x=\ln30\\\ln(2x)^2-\ln10x=\ln30\\\ln\dfrac{4x^2}{10x}=\ln30\\\ln\dfrac{2x}{5}=\ln30\iff\dfrac{2}{5}x=30\ \ \ \multiply\ both\ sides\ by\ \dfrac{5}{3}\\\boxed{x=75}\in D\)
