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