$$\left. \begin{array} { l } { a = x ^ { n + y } , b = x ^ { * } + , y ^ { n } c = x ^ { p } + y , a ^ { q - r } \times b ^ { - p } \times y - x \times b } \\ { x y z = 1 , \text { p r o v \right.$$
$\left\{\begin{matrix}x=b\text{, }y=\frac{2\pi n_{1}i}{\ln(b)}+\log_{b}\left(a\right)-n\text{, }n_{1}\in \mathrm{Z}\text{, }&a\neq 0\text{ and }b\neq 1\text{ and }b\neq 0\\x=b\text{, }y\in \mathrm{C}\text{, }&\left(b=0\text{ and }a=0\right)\text{ or }\left(b=1\text{ and }a=1\right)\end{matrix}\right.$
$\left\{\begin{matrix}x=b\text{, }y=\log_{b}\left(a\right)-n\text{, }&a>0\text{ and }b\neq 1\text{ and }b>0\\x=-1\text{, }y\in \mathrm{R}\text{, }&b=-1\text{ and }a=-1\\x=1\text{, }y\in \mathrm{R}\text{, }&a=1\text{ and }b=1\\x=0\text{, }y>-n\text{, }&b=0\text{ and }a=0\end{matrix}\right.$
