Solve {l}{log_{3}(ex^2+piy^2)=3+log_{2}5}{log_{3}(x+y)-log_{3}(x-y)=log_{3}2}

$$\left\{ \begin{array} { l } { \log _ { 3 } ( e x ^ { 2 } + \pi y ^ { 2 } ) = 3 + \log _ { 2 } 5 } \\ { \log _ { 3 } ( x + y ) - \log _ { 3 } ( x - y ) = \log _ { 3 } 2 } \end{array} \right.$$

Solve for x, y (complex solution)

$$x=9i\sqrt{-\frac{3\times 5^{\log_{2}\left(3\right)}}{\pi +9e}}\approx -10.62235967\text{, }y=3i\sqrt{-\frac{3\times 5^{\log_{2}\left(3\right)}}{\pi +9e}}\approx -3.540786557$$

$$x=-9i\sqrt{-\frac{3\times 5^{\log_{2}\left(3\right)}}{\pi +9e}}\approx 10.62235967\text{, }y=-3i\sqrt{-\frac{3\times 5^{\log_{2}\left(3\right)}}{\pi +9e}}\approx 3.540786557\text{, }\sqrt{-3\times 5^{\log_{2}\left(3\right)}}\neq 0$$

Solve for x, y

$$x=9\times 5^{\frac{\log_{2}\left(3\right)}{2}}\sqrt{\frac{3}{\pi +9e}}\approx 10.62235967$$

$$y=3\times 5^{\frac{\log_{2}\left(3\right)}{2}}\sqrt{\frac{3}{\pi +9e}}\approx 3.540786557$$