Why is a weak basic drug more soluble in aqueous acidic solution?
The fact that they are drugs does not alter the reason. However given that they are drugs they will almost certainly not be strong acids and bases, and will not dissociate completely, hence behaving as a weak acid or base. Acids are less soluble at low pH because the solution already contains H+ ions. According to the law of mass action the addition of more H+ will move the equilibrium to the undissociated form, keeping it less soluble. At high ph the opposite occurs, the OH- present will remove the H+ ( as H2O) so encouraging more acid to dissolve.Bases are the same but opposite.