$\log(\frac{x+y}{3})=\frac{\log(xy)}{2}\text{ and }\frac{\log(xy)}{2}=7$

$\left\{\begin{matrix}x=15000000-5000000\sqrt{5}\text{, }&y=5000000\sqrt{5}+15000000\\x=5000000\sqrt{5}+15000000\text{, }&y=15000000-5000000\sqrt{5}\end{matrix}\right.$

$\left\{\begin{matrix}y=15000000-5000000\sqrt{5}\text{, }&x=5000000\sqrt{5}+15000000\\y=5000000\sqrt{5}+15000000\text{, }&x=15000000-5000000\sqrt{5}\end{matrix}\right.$