Résoudre v^x=12

$$v ^ { x } = 12$$

Calculer v (solution complexe)

$$v=e^{-\frac{2\pi n_{1}\left(Im(x)+iRe(x)\right)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}\times 12^{\frac{Re(x)-iIm(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}$$

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

Calculer x (solution complexe)

$$x=\frac{2\pi n_{1}i}{\ln(v)}+\log_{v}\left(12\right)$$

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

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

Calculer v

$$\left\{\begin{matrix}v=-12^{\frac{1}{x}}\text{, }&x\neq 0\text{ and }Numerator(x)\text{bmod}2=0\text{ and }Denominator(x)\text{bmod}2=1\\v=12^{\frac{1}{x}}\text{, }&x\neq 0\end{matrix}\right,$$

Calculer x

$$x=\log_{v}\left(12\right)$$

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