solve ln(x)<1 in ]-5,10[
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
Candidates, pending the domain check: x < e
For the expression ln(x) to exist, you must check: x > 0
Domain constraints: x > 0
Let's create the table of the different solutions to find the overall solution:
x-∞ -5 0 e 10 +∞
x ∈ (0, e)❌❌❌❌✅❌❌❌❌
x > -5❌❌✅✅✅✅✅✅✅
x < 10✅✅✅✅✅✅✅❌❌
Global solution❌❌❌❌✅❌❌❌❌
▶Solution:   x ∈ (0, e)
2) The numeric value of: x ∈ (0, e) is:
▷ x ∈ (0, ≈ 2.7183)