Hamiltonian after Co-ordinate Transformation

Question

I have come across this problem in a textbook; $$\dot{x}=ax-bxy$$ $$\dot{y}=-cy+dxy$$ I am asked to show that the transformation $(x,y)\to(p,q)$ where $p=\ln{x}$ and $q=\ln{y}$ leads to a Hamiltonian system, where $H=be^p-cp+be^p-aq$. My attempt at this question hasn't gone so well, I have not done much with hamiltonian dynamics, and in fact this is the first question I'm doing concerning the field. I firstly label $$f(x,y)=ax-bxy$$ And, $$g(x,y)=-cy+dxy$$ Then the system is hamiltonian if $$\frac{\partial f}{\partial x}=-\frac{\partial g}{\partial y}$$ When calculating the partial derivatives however, I am finding that; $$\frac{\partial f}{\partial x}\neq -\frac{\partial g}{\partial y}$$ My main problem is showing that this equality holds. After this what will I need to do to find the function $H$?