Risolvi l^alpha=pi^3+pi^4

$$l ^ { \alpha } = \pi ^ { 3 } + \pi ^ { 4 }$$

Trova l (soluzione complessa)

$$l=e^{-\frac{2\pi n_{1}\left(Im(\alpha )+iRe(\alpha )\right)}{\left(Re(\alpha )\right)^{2}+\left(Im(\alpha )\right)^{2}}}\pi ^{\frac{3\left(Re(\alpha )-iIm(\alpha )\right)}{\left(Re(\alpha )\right)^{2}+\left(Im(\alpha )\right)^{2}}}\left(\pi +1\right)^{\frac{Re(\alpha )-iIm(\alpha )}{\left(Re(\alpha )\right)^{2}+\left(Im(\alpha )\right)^{2}}}$$

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

Trova α (soluzione complessa)

$$\alpha =\frac{2\pi n_{1}i}{\ln(l)}+\frac{\ln(\pi +1)+3\ln(\pi )}{\ln(l)}$$

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

$$l\neq 1\text{ and }l\neq 0$$

Trova l

$$\left\{\begin{matrix}l=-\left(\pi ^{3}\left(\pi +1\right)\right)^{\frac{1}{\alpha }}\text{, }&\alpha \neq 0\text{ and }Numerator(\alpha )\text{bmod}2=0\text{ and }Denominator(\alpha )\text{bmod}2=1\\l=\left(\pi ^{3}\left(\pi +1\right)\right)^{\frac{1}{\alpha }}\text{, }&\alpha \neq 0\end{matrix}\right,$$

Trova α

$$\alpha =\frac{\ln(\pi +1)+3\ln(\pi )}{\ln(l)}$$

$$l\neq 1\text{ and }l>0$$