Solve for f (complex solution)
\left\{\begin{matrix}f=\frac{\ln(x+1)}{gx}\text{, }&x\neq 0\text{ and }g\neq 0\text{ and }x\neq -1\\f\in \mathrm{C}\text{, }&x=0\end{matrix}\right.
Solve for g (complex solution)
\left\{\begin{matrix}g=\frac{\ln(x+1)}{fx}\text{, }&x\neq 0\text{ and }f\neq 0\text{ and }x\neq -1\\g\in \mathrm{C}\text{, }&x=0\end{matrix}\right.
Solve for f
\left\{\begin{matrix}f=\frac{\ln(x+1)}{gx}\text{, }&x\neq 0\text{ and }g\neq 0\text{ and }x>-1\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
Solve for g
\left\{\begin{matrix}g=\frac{\ln(x+1)}{fx}\text{, }&x\neq 0\text{ and }f\neq 0\text{ and }x>-1\\g\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
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