Solve for a (complex solution)
\left\{\begin{matrix}a=-\frac{\ln(2x-7)-\ln(x+2)-\ln(7)}{\ln(7)g_{7}\left(x-2\right)}\text{, }&x\neq 2\text{ and }g_{7}\neq 0\text{ and }x\neq -2\text{ and }x\neq \frac{7}{2}\\a\in \mathrm{C}\text{, }&x=-\frac{21}{5}\text{ and }g_{7}=0\end{matrix}\right.
Solve for g_7 (complex solution)
\left\{\begin{matrix}g_{7}=-\frac{\ln(2x-7)-\ln(x+2)-\ln(7)}{\ln(7)a\left(x-2\right)}\text{, }&x\neq 2\text{ and }a\neq 0\text{ and }x\neq -2\text{ and }x\neq \frac{7}{2}\\g_{7}\in \mathrm{C}\text{, }&x=-\frac{21}{5}\text{ and }a=0\end{matrix}\right.
Solve for a
a=-\frac{\ln(2x-7)-\ln(x+2)-\ln(7)}{\ln(7)g_{7}\left(x-2\right)}
g_{7}\neq 0\text{ and }x>\frac{7}{2}
Solve for g_7
g_{7}=-\frac{\ln(2x-7)-\ln(x+2)-\ln(7)}{\ln(7)a\left(x-2\right)}
a\neq 0\text{ and }x>\frac{7}{2}
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