Résoudre a-121=b^x

$$a - 121 = b ^ { x }$$

Calculer a (solution complexe)

$$a=b^{x}+121$$

Calculer b (solution complexe)

$$b=e^{\frac{Im(x)arg(a-121)+iRe(x)arg(a-121)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}-\frac{2\pi n_{1}iRe(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}-\frac{2\pi n_{1}Im(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}\left(|a-121|\right)^{\frac{Re(x)-iIm(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}$$

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

Calculer a

$$a=b^{x}+121$$

$$\left(b<0\text{ and }Denominator(x)\text{bmod}2=1\right)\text{ or }\left(b=0\text{ and }x>0\right)\text{ or }b>0$$

Calculer b

$$\left\{\begin{matrix}b=\left(a-121\right)^{\frac{1}{x}}\text{, }&\left(Numerator(x)\text{bmod}2=1\text{ and }Denominator(x)\text{bmod}2=1\text{ and }a<121\text{ and }\left(a-121\right)^{\frac{1}{x}}\neq 0\right)\text{ or }\left(\left(a-121\right)^{\frac{1}{x}}<0\text{ and }a>121\text{ and }x\neq 0\text{ and }Denominator(x)\text{bmod}2=1\right)\text{ or }\left(a=121\text{ and }x>0\right)\text{ or }\left(\left(a-121\right)^{\frac{1}{x}}>0\text{ and }a>121\text{ and }x\neq 0\right)\\b=-\left(a-121\right)^{\frac{1}{x}}\text{, }&\left(a<121\text{ and }Numerator(x)\text{bmod}2=1\text{ and }Numerator(x)\text{bmod}2=0\text{ and }Denominator(x)\text{bmod}2=1\text{ and }\left(a-121\right)^{\frac{1}{x}}\neq 0\right)\text{ or }\left(a>121\text{ and }x\neq 0\text{ and }\left(a-121\right)^{\frac{1}{x}}>0\text{ and }Numerator(x)\text{bmod}2=0\text{ and }Denominator(x)\text{bmod}2=1\right)\text{ or }\left(Numerator(x)\text{bmod}2=0\text{ and }a=121\text{ and }x>0\right)\text{ or }\left(a>121\text{ and }x\neq 0\text{ and }\left(a-121\right)^{\frac{1}{x}}<0\text{ and }Numerator(x)\text{bmod}2=0\right)\\b\neq 0\text{, }&x=0\text{ and }a=122\end{matrix}\right,$$