ln : ]0;+∞[ ⟶ ℝ
x ⟼ ln(x) The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718281828459.
Properties
- ln(1) = 0
- ln(e) = 1
- ln(xy) = ln(x) + ln(y) for x > 0 and y > 0
- ln(x / y) = ln(x) − ln(y) for x > 0 and y > 0
- ln(x ^ y) = y ln(x) for x > 0
- ∀(x,y) ∈ ]0;+∞[², x < y ⇒ ln(x) < ln(y)
- (ln(x))' = 1/x for x > 0
- If u(x) strictly positive, (ln(u))' = u'(x) / u(x)
