ln(x)+ln(-x)=0
1) Let's solve in ℝ: ln(x) + ln(-x) = 0
2) Let's find the domain of ln(x) + ln(-x) = 0
For the expression ln(x) to exist, you must check: x > 0
For the expression ln(-x) to be defined, we must have: -x > 0
Solution obtained: x > 0
3) Let's solve in ℝ: -x > 0
ⓘ We add x to both sides
0 > x
Solution found: x < 0
No value of x satisfies both x > 0 and x < 0
Domain constraints: x ∈ ∅
The expressions have no common domain: there is no solution
▶Solution:   x ∈ ∅