I am working on an optimization problem where I aim to maximize revenue. My current model has the following objective function: $$ Sales(P_i) * log(P_i - const_i))$$ where $P_i$ represents the price of product $i$. The Sales function is a mixed integer linear function due to the inclusion of some categorical variables. I should note also that Sales function, which is linear, is modeled to predict the log of sales (a common practice in econometrics) hence the need to log the unit margin part in order to obtain the true optimum.
Is there a way to transform this objective function into a quadratic form so I can use quadratic solvers? If not, is there any approximation that I can do?