Solve alog(Rx)=b

$$a \log ( R x ) = b$$

Solve for R

$$\left\{\begin{matrix}R=\frac{10^{\frac{b}{a}}}{x}\text{, }&a\neq 0\text{ and }x\neq 0\\R>0\text{, }&x>0\text{ and }b=0\text{ and }a=0\\R<0\text{, }&x<0\text{ and }b=0\text{ and }a=0\end{matrix}\right.$$

Solve for a

$$\left\{\begin{matrix}a=b\log_{Rx}\left(10\right)\text{, }&\left(R\neq \frac{1}{x}\text{ and }R>0\text{ and }x>0\right)\text{ or }\left(R\neq \frac{1}{x}\text{ and }R<0\text{ and }x<0\right)\\a\in \mathrm{R}\text{, }&b=0\text{ and }R=\frac{1}{x}\text{ and }x\neq 0\end{matrix}\right.$$