$\left\{\begin{matrix}x=\frac{2\pi n_{1}i}{\ln(a)}+5\text{, }n_{1}\in \mathrm{Z}\text{, }&a\neq 0\text{ and }a\neq 1\\x\in \mathrm{C}\text{, }&a=0\text{ or }a=1\\x\neq 0\text{, }&a=0\end{matrix}\right.$

$\left\{\begin{matrix}\\a=1\text{, }&\text{unconditionally}\\a=-1\text{, }&Denominator(x)\text{bmod}2=1\text{ and }Numerator(x)\text{bmod}2=1\\a=0\text{, }&x>0\\a\neq 0\text{, }&x=5\end{matrix}\right.$

$\left\{\begin{matrix}x>0\text{, }&a=0\\x=5\text{, }&a\neq 0\\x\in \mathrm{R}\text{, }&a=1\text{ or }\left(a=-1\text{ and }Numerator(x)\text{bmod}2=1\text{ and }Denominator(x)\text{bmod}2=1\right)\end{matrix}\right.$