Resol H=ln(R/S)/ln(N)

$$H = \ln ( \frac { R } { S } ) / \ln ( N )$$

Resoleu H

$$H=\log_{N}\left(\frac{R}{S}\right)$$

$$\left(N\neq 1\text{ and }N>0\text{ and }R<0\text{ and }S<0\right)\text{ or }\left(N\neq 1\text{ and }N>0\text{ and }R>0\text{ and }S>0\right)$$

Resoleu N

$$\left\{\begin{matrix}N=\left(\frac{R}{S}\right)^{\frac{1}{H}}\text{, }&\left(\left(\frac{R}{S}\right)^{\frac{1}{H}}>0\text{ and }\left(\frac{R}{S}\right)^{\frac{1}{H}}-1<0\text{ and }H\neq 0\text{ and }R>0\text{ and }S>0\text{ and }R\neq S\right)\text{ or }\left(H\neq 0\text{ and }R>0\text{ and }S>0\text{ and }R\neq S\text{ and }\left(\frac{R}{S}\right)^{\frac{1}{H}}-1>0\right)\text{ or }\left(\left(\frac{R}{S}\right)^{\frac{1}{H}}>0\text{ and }\left(\frac{R}{S}\right)^{\frac{1}{H}}-1<0\text{ and }H\neq 0\text{ and }R<0\text{ and }S<0\text{ and }R\neq S\right)\text{ or }\left(H\neq 0\text{ and }R<0\text{ and }S<0\text{ and }R\neq S\text{ and }\left(\frac{R}{S}\right)^{\frac{1}{H}}-1>0\right)\\N\in \left(0,1\right)\cup \left(1,\infty\right)\text{, }&H=0\text{ and }R=S\text{ and }S\neq 0\end{matrix}\right,$$