ln(-x)>1
Let's solve in ℝ: ln(-x) > 1
On the logarithm's domain, ln is strictly increasing: ln(-x) > 1 is equivalent to -x > e
ⓘ We add x and subtract e from both sides
-e > x
Candidates, pending the domain check: x < -e
Let's find the domain of ln(-x) > 1
For the expression ln(-x) to be defined, we must have: -x > 0
ⓘ We add x to both sides
0 > x
Domain constraints: x < 0
▶Solution:   x < -e
The numeric value of: x < -e equals:
▷ x < -2.7183 (approximate value)