Solve for P_3 (complex solution)
\left\{\begin{matrix}P_{3}=\frac{2\pi n_{1}i}{\ln(s_{3})}+\log_{s_{3}}\left(U\right)\text{, }n_{1}\in \mathrm{Z}\text{, }&U\neq 0\text{ and }s_{3}\neq 1\text{ and }s_{3}\neq 0\\P_{3}\in \mathrm{C}\text{, }&\left(s_{3}=0\text{ and }U=0\right)\text{ or }\left(s_{3}=1\text{ and }U=1\right)\end{matrix}\right.
Solve for U (complex solution)
U=s_{3}^{P_{3}}
Solve for P_3
\left\{\begin{matrix}P_{3}=\log_{s_{3}}\left(U\right)\text{, }&U>0\text{ and }s_{3}\neq 1\text{ and }s_{3}>0\\P_{3}\in \mathrm{R}\text{, }&\left(s_{3}=1\text{ and }U=1\right)\text{ or }\left(s_{3}=-1\text{ and }U=-1\text{ and }Denominator(P_{3})\text{bmod}2=1\text{ and }Numerator(P_{3})\text{bmod}2=1\right)\\P_{3}>0\text{, }&s_{3}=0\text{ and }U=0\end{matrix}\right.
Solve for U
U=s_{3}^{P_{3}}
\left(s_{3}<0\text{ and }Denominator(P_{3})\text{bmod}2=1\right)\text{ or }\left(s_{3}=0\text{ and }P_{3}>0\right)\text{ or }s_{3}>0
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