smc

The domain of the LHS implies that $$40<x<60$$ Begin from the left hand side $${\log }_{10}[(x-40)(60-x)]<2$$ $$(x-40)(60-x)<100$$ $$-x^2+100x-2500<0$$ $$(x-50{)}^2>0$$ $$x\ne 50$$ Hence, we have integers from 41 to 49 and 51 to 59. There are $\boxed{18}$ integers.