حل log_{3}({eleft(3yright)^2+piy^2})-log_{2}({5})=3

$$\log_{ 3 }({ e { \left(3y \right) }^{ 2 } + \pi { y }^{ 2 } }) - \log_{ 2 }({ 5 }) = 3$$

برای y حل کنید (complex solution)

$$y=-3i\sqrt{-\frac{3^{\log_{2}\left(5\right)+1}}{\pi +9e}}\approx 3.540786557$$

$$y=3i\sqrt{-\frac{3^{\log_{2}\left(5\right)+1}}{\pi +9e}}\approx -3.540786557\text{, }\sqrt{-3\times 3^{\log_{2}\left(5\right)}}\neq 0$$

برای y حل کنید

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

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