0Where did you get the word "universe"? Surely the definition should have been given where it was introduced. Is this a translation to English from another language? I suspect it is what I would call the "domain" of a function. That is defined as the set of all number to which the function can be applied. The crucial point is that logarithm to any base has domain "all positive numbers".
So "log2(x2+ 2x)" has domain x2+ 2x= x(x+ 2)> 0. A product of two numbers is positive if and only if the two numbers have the same sign, both positive of both negative: x> 0 and x+ 2> 0 so x> 0 and x> -2. Both are true for x> 0,
Or x< 0 and x+ 2< 0 so x< 0 and x< -2. Both are true for x< -2.