Solve for k (complex solution)
\left\{\begin{matrix}k=\frac{2\pi n_{1}i}{\ln(y)}+\log_{y}\left(t\right)\text{, }n_{1}\in \mathrm{Z}\text{, }&t\neq 0\text{ and }y\neq 1\text{ and }y\neq 0\\k\in \mathrm{C}\text{, }&\left(y=0\text{ and }t=0\right)\text{ or }\left(y=1\text{ and }t=1\right)\end{matrix}\right.
Solve for t (complex solution)
t=y^{k}
Solve for k
\left\{\begin{matrix}k=\log_{y}\left(t\right)\text{, }&t>0\text{ and }y\neq 1\text{ and }y>0\\k\in \mathrm{R}\text{, }&\left(y=1\text{ and }t=1\right)\text{ or }\left(y=-1\text{ and }t=-1\text{ and }Denominator(k)\text{bmod}2=1\text{ and }Numerator(k)\text{bmod}2=1\right)\\k>0\text{, }&y=0\text{ and }t=0\end{matrix}\right.
Solve for t
t=y^{k}
\left(y<0\text{ and }Denominator(k)\text{bmod}2=1\right)\text{ or }\left(y=0\text{ and }k>0\right)\text{ or }y>0
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