Solve {l}{lnP+gammalnV=lnK}{1/PdP+gamma/VdV=0}{dP/P=-1.4*dV/V}

$$\left. \begin{array} { l } { \ln P + \gamma \ln V = \ln K } \\ { \frac { 1 } { P } d P + \frac { \gamma } { V } d V = 0 } \\ { \frac { d P } { P } = - 1.4 \times \frac { d V } { V } } \end{array} \right.$$

Solve for P, γ, V, K, d (complex solution)

$$\left\{\begin{matrix}P=KV\text{, }\gamma =-1\text{, }V\neq 0\text{, }K\neq 0\text{, }d=0\text{, }&K\neq 0\text{ and }V\neq 0\text{ and }Im(\ln(KV))-Im(\ln(K))-Im(\ln(V))=0\\P=\frac{K}{e^{\gamma \ln(V)}}\text{, }\gamma \in \mathrm{C}\text{, }V\neq 0\text{, }K\neq 0\text{, }d=0\text{, }&Im(\ln(\frac{K}{e^{\gamma \ln(V)}}))+Re(\gamma )Im(\ln(V))+Im(\gamma )Re(\ln(V))-Im(\ln(K))=0\text{ and }V\neq 0\text{ and }K\neq 0\end{matrix}\right.$$

Solve for P, γ, V, K, d

$$\left\{\begin{matrix}P=\frac{K}{V^{\gamma }}\text{, }\gamma \geq 0\text{, }V>0\text{, }K>0\text{, }d=0\text{, }&\left(K\neq 0\text{ and }V>0\right)\text{ or }\left(K\neq 0\text{ and }V<0\text{ and }Denominator(\gamma )\text{bmod}2=1\right)\text{ or }\left(V=0\text{ and }\gamma <0\right)\\P=\frac{K}{V^{\gamma }}\text{, }\gamma \in \mathrm{R}\text{, }V>0\text{, }K>0\text{, }d=0\text{, }&K\neq 0\text{ and }\left(V>0\text{ or }Denominator(\gamma )\text{bmod}2=1\right)\text{ and }V\neq 0\end{matrix}\right.$$