log(x) = 3-log(100x+900) ============> x = x*(100x + 900) = 1000 100x^2 + 900x = 1000 x^2 + 9x - 10 = 0 (x+10)*(x-1) = 0. The roots are x= -10 and x= 1. Only positive root makes sense. Answer. The only solution is x = 1.