I have a strange problem. Have this example. log(x-2)+log(x+1)=0 Domain of these functions are: x>2, x>-1 resulting in x>2; by logarithm rule we can combine these 2 logarithms and make one logarithm. log(x-2)(x+1)=0 (-infinity,-1) U (2,+infinity) But the domain of this changes. How can we combine these 2 logarithms if the domain changes? Am I missing something here?