Solve a^b+c=x

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

Solve for a (complex solution)

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

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

Solve for b (complex solution)

$$\left\{\begin{matrix}b=\frac{2\pi n_{1}i}{\ln(a)}+\log_{a}\left(x-c\right)\text{, }n_{1}\in \mathrm{Z}\text{, }&c\neq x\text{ and }a\neq 1\text{ and }a\neq 0\\b\in \mathrm{C}\text{, }&\left(a=0\text{ and }c=x\right)\text{ or }\left(a=1\text{ and }c=x-1\right)\end{matrix}\right.$$

Solve for b

$$\left\{\begin{matrix}b=\log_{a}\left(x-c\right)\text{, }&c<x\text{ and }a\neq 1\text{ and }a>0\\b\in \mathrm{R}\text{, }&\left(a=1\text{ and }c=x-1\right)\text{ or }\left(a=-1\text{ and }c=x+1\text{ and }Denominator(b)\text{bmod}2=1\text{ and }Numerator(b)\text{bmod}2=1\right)\\b>0\text{, }&a=0\text{ and }c=x\end{matrix}\right.$$