Solucionar log_{r}(x-1)=mu

$$\log _ { r } ( x - 1 ) = \mu$$

Resolver para r

$$\left\{\begin{matrix}r=\left(x-1\right)^{\frac{1}{\mu }}\text{, }&\mu \neq 0\text{ and }x>1\text{ and }x\neq 2\text{ and }\left(\left(x-1\right)^{\frac{1}{\mu }}-1>0\text{ or }\left(x-1\right)^{\frac{1}{\mu }}>0\right)\text{ and }\left(x-1\right)^{\frac{1}{\mu }}-1\neq 0\\r\in \left(0,1\right)\cup \left(1,\infty\right)\text{, }&x=2\text{ and }\mu =0\end{matrix}\right,$$

Resolver para x

$$x=r^{\mu }+1$$

$$r^{\mu }+1>1\text{ and }r\neq 1\text{ and }r>0$$