Vyriešiť log_{3}({ex^2+9y^2})+log_{3}({5})=3

$$\log_{ 3 }({ e { x }^{ 2 } +9 { y }^{ 2 } }) + \log_{ 3 }({ 5 }) = 3$$

Riešenie pre x (complex solution)

$$x=-\frac{3i\sqrt{\frac{5\left(5y^{2}-3\right)}{e}}}{5}$$

$$x=\frac{3i\sqrt{\frac{5\left(5y^{2}-3\right)}{e}}}{5}$$

Riešenie pre y (complex solution)

$$y=-\frac{\sqrt{135-25ex^{2}}}{15}$$

$$y=\frac{\sqrt{135-25ex^{2}}}{15}$$

Riešenie pre x

$$x=\frac{3\sqrt{\frac{5\left(3-5y^{2}\right)}{e}}}{5}$$

$$x=-\frac{3\sqrt{\frac{5\left(3-5y^{2}\right)}{e}}}{5}\text{, }\left(y\neq 0\text{ and }|y|\leq \frac{\sqrt{15}}{5}\right)\text{ or }|y|<\frac{\sqrt{15}}{5}$$

Riešenie pre y

$$y=\frac{\sqrt{135-25ex^{2}}}{15}$$

$$y=-\frac{\sqrt{135-25ex^{2}}}{15}\text{, }\left(x\neq 0\text{ and }|x|\leq \frac{9}{\sqrt{15e}}\right)\text{ or }|x|<\frac{9}{\sqrt{15e}}$$