Résoudre log_{3}(ex^2+piy^2)=3+log_{3}5

$$\log _ { 3 } ( e x ^ { 2 } + \pi y ^ { 2 } ) = 3 + \log _ { 3 } 5$$

Calculer x (solution complexe)

$$x=-i\sqrt{\frac{\pi y^{2}-135}{e}}$$

$$x=i\sqrt{\frac{\pi y^{2}-135}{e}}$$

Calculer y (solution complexe)

$$y=-i\sqrt{\frac{ex^{2}-135}{\pi }}$$

$$y=i\sqrt{\frac{ex^{2}-135}{\pi }}$$

Calculer x

$$x=\sqrt{\frac{135-\pi y^{2}}{e}}$$

$$x=-\sqrt{\frac{135-\pi y^{2}}{e}}\text{, }|y|<\frac{45}{\sqrt{15\pi }}\text{ or }\left(y\neq 0\text{ and }|y|\leq \frac{45}{\sqrt{15\pi }}\right)$$

Calculer y

$$y=\sqrt{\frac{135-ex^{2}}{\pi }}$$

$$y=-\sqrt{\frac{135-ex^{2}}{\pi }}\text{, }|x|<\frac{45}{\sqrt{15e}}\text{ or }\left(x\neq 0\text{ and }|x|\leq \frac{45}{\sqrt{15e}}\right)$$