다음을 풀어보세요: log_{3}(ex^2+9y^2)+log_{2}5=3

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

x에 대한 해 (complex solution)

$$x=-3\sqrt{\frac{3^{-\log_{2}\left(5\right)+1}-y^{2}}{e}}$$

$$x=3\sqrt{\frac{3^{-\log_{2}\left(5\right)+1}-y^{2}}{e}}$$

y에 대한 해 (complex solution)

$$y=-\frac{\sqrt{-ex^{2}+\frac{27}{3^{\log_{2}\left(5\right)}}}}{3}$$

$$y=\frac{\sqrt{-ex^{2}+\frac{27}{3^{\log_{2}\left(5\right)}}}}{3}$$

x에 대한 해

$$x=3^{-\frac{\log_{2}\left(5\right)}{2}+1}\sqrt{\frac{3-3^{\log_{2}\left(5\right)}y^{2}}{e}}$$

$$x=-3^{-\frac{\log_{2}\left(5\right)}{2}+1}\sqrt{\frac{3-3^{\log_{2}\left(5\right)}y^{2}}{e}}\text{, }|y|<3^{\frac{-\log_{2}\left(5\right)+1}{2}}\text{ or }\left(y\neq 0\text{ and }|y|\leq 3^{\frac{-\log_{2}\left(5\right)+1}{2}}\right)$$

y에 대한 해

$$y=\frac{3^{-\frac{\log_{2}\left(5\right)}{2}}\sqrt{27-e\times 3^{\log_{2}\left(5\right)}x^{2}}}{3}$$

$$y=-\frac{3^{-\frac{\log_{2}\left(5\right)}{2}}\sqrt{27-e\times 3^{\log_{2}\left(5\right)}x^{2}}}{3}\text{, }|x|\leq \frac{3^{\frac{-\log_{2}\left(5\right)+3}{2}}}{\sqrt{e}}$$