In Finkelstein reaction, how does precipitate formation favor forward reaction?
$\ce{NaCl} $ and $\ce{NaBr }$formed as products are polar compounds which are vey less soluble in non- polar solvents like dry acetone, but $\ce{NaI } $due to high polarizability of $\ce {I^-} $ is soluble in acetone. So the products precipitate.  If a reaction is in equilibrium in constant temperature  and it is distorted somehow, it goes in the direction to nullify the effect of distortion.  This is the Le-Chattelier's principle.  If some of the products are removed to keep the $\ce{K_c}$ constant , some more reactants will react and convert into products. Thus constant removal of products by precipitation helps to dissociate reactants into products and thus favour the forward reaction.