Résoudre frac{log_{2}50}{x^3}=y^x

$$\frac { \log _ { 2 } 50 } { x ^ { 3 } } = y ^ { x }$$

Calculer y (solution complexe)

$$y=e^{-\frac{2\pi n_{1}iRe(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}-\frac{2\pi n_{1}Im(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}+\frac{arg(\frac{1}{x^{3}})Im(x)+iarg(\frac{1}{x^{3}})Re(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}\left(2\log_{2}\left(5\right)+1\right)^{\frac{Re(x)-iIm(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}\left(|x|\right)^{\frac{3\left(-Re(x)+iIm(x)\right)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}$$

$$n_{1}\in \mathrm{Z}$$

$$x\neq 0$$

Calculer y

$$\left\{\begin{matrix}y=\left(\frac{2\log_{2}\left(5\right)+1}{x^{3}}\right)^{\frac{1}{x}}\text{, }&\left(\left(\frac{2\log_{2}\left(5\right)+1}{x^{3}}\right)^{\frac{1}{x}}<0\text{ and }Denominator(x)\text{bmod}2=1\text{ and }x>0\right)\text{ or }\left(Numerator(x)\text{bmod}2=1\text{ and }Denominator(x)\text{bmod}2=1\text{ and }x<0\right)\text{ or }\left(x>0\text{ and }\left(\frac{2\log_{2}\left(5\right)+1}{x^{3}}\right)^{\frac{1}{x}}>0\right)\\y=-\left(\frac{2\log_{2}\left(5\right)+1}{x^{3}}\right)^{\frac{1}{x}}\text{, }&\left(\left(\frac{2\log_{2}\left(5\right)+1}{x^{3}}\right)^{\frac{1}{x}}>0\text{ and }Numerator(x)\text{bmod}2=0\text{ and }Denominator(x)\text{bmod}2=1\text{ and }x>0\right)\text{ or }\left(Numerator(x)\text{bmod}2=1\text{ and }x<0\text{ and }Numerator(x)\text{bmod}2=0\text{ and }Denominator(x)\text{bmod}2=1\right)\text{ or }\left(Numerator(x)\text{bmod}2=0\text{ and }x>0\text{ and }\left(\frac{2\log_{2}\left(5\right)+1}{x^{3}}\right)^{\frac{1}{x}}<0\right)\end{matrix}\right,$$