Solve W=klog_{e}frac{V_{2}}{V_{1}}

$$W = k \log _ { e } \frac { V _ { 2 } } { V _ { 1 } }$$

Solve for V_1

$$\left\{\begin{matrix}V_{1}=V_{2}e^{-\frac{W}{k}}\text{, }&V_{2}\neq 0\text{ and }k\neq 0\\V_{1}>0\text{, }&V_{2}>0\text{ and }W=0\text{ and }k=0\\V_{1}<0\text{, }&V_{2}<0\text{ and }W=0\text{ and }k=0\end{matrix}\right.$$

Solve for V_2

$$\left\{\begin{matrix}V_{2}=V_{1}e^{\frac{W}{k}}\text{, }&k\neq 0\text{ and }V_{1}\neq 0\\V_{2}>0\text{, }&V_{1}>0\text{ and }W=0\text{ and }k=0\\V_{2}<0\text{, }&V_{1}<0\text{ and }W=0\text{ and }k=0\end{matrix}\right.$$