Solve operatorname{og}_{6}22=log_{6}(5x-8)

$$\operatorname { og } _ { 6 } 22 = \log _ { 6 } ( 5 x - 8 )$$

Solve for g_6 (complex solution)

$$\left\{\begin{matrix}g_{6}=\frac{\log_{6}\left(5x-8\right)}{22o}\text{, }&o\neq 0\text{ and }x\neq \frac{8}{5}\\g_{6}\in \mathrm{C}\text{, }&o=0\text{ and }x=\frac{9}{5}\end{matrix}\right.$$

Solve for o (complex solution)

$$\left\{\begin{matrix}o=\frac{\log_{6}\left(5x-8\right)}{22g_{6}}\text{, }&g_{6}\neq 0\text{ and }x\neq \frac{8}{5}\\o\in \mathrm{C}\text{, }&g_{6}=0\text{ and }x=\frac{9}{5}\end{matrix}\right.$$

Solve for g_6

$$\left\{\begin{matrix}g_{6}=\frac{\log_{6}\left(5x-8\right)}{22o}\text{, }&o\neq 0\text{ and }x>\frac{8}{5}\\g_{6}\in \mathrm{R}\text{, }&o=0\text{ and }x=\frac{9}{5}\end{matrix}\right.$$

Solve for o

$$\left\{\begin{matrix}o=\frac{\log_{6}\left(5x-8\right)}{22g_{6}}\text{, }&g_{6}\neq 0\text{ and }x>\frac{8}{5}\\o\in \mathrm{R}\text{, }&g_{6}=0\text{ and }x=\frac{9}{5}\end{matrix}\right.$$