Розв'яжіть x^alpha=25

$$x ^ { \alpha } = 25$$

Знайдіть x (complex solution)

$$x=e^{-\frac{2\pi n_{1}\left(Im(\alpha )+iRe(\alpha )\right)}{\left(Re(\alpha )\right)^{2}+\left(Im(\alpha )\right)^{2}}}\times 5^{\frac{2\left(Re(\alpha )-iIm(\alpha )\right)}{\left(Re(\alpha )\right)^{2}+\left(Im(\alpha )\right)^{2}}}$$

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

Знайдіть α (complex solution)

$$\alpha =\frac{2\pi n_{1}i}{\ln(x)}+2\log_{x}\left(5\right)$$

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

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

Знайдіть x

$$\left\{\begin{matrix}x=-25^{\frac{1}{\alpha }}\text{, }&\alpha \neq 0\text{ and }Numerator(\alpha )\text{bmod}2=0\text{ and }Denominator(\alpha )\text{bmod}2=1\\x=25^{\frac{1}{\alpha }}\text{, }&\alpha \neq 0\end{matrix}\right,$$

Знайдіть α

$$\alpha =2\log_{x}\left(5\right)$$

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