EXP017 · Powers, exponents & logarithms · Classes 11–12 + B.Tech
Natural Logarithm (base e)
The natural logarithm ln x uses base e ≈ 2.718. It is the logarithm that calculus prefers: the slope of ln x is 1/x.
ln xNatural Logarithm (base e)
📐 Formula
ln x = y ⇔ eʸ = x; ln e = 1, ln 1 = 0
✏️ Worked example
ln 10 ≈ 2.303, because e^2.303 ≈ 10.
🌍 Where it is used
Continuous growth, half-life formulas, information theory.
❓ Quick check
ln(e³) = ?
🏋️ Practice
Easyln 1 = ?
Answer: 0
MediumSolve eˣ = 5.
Answer: x = ln 5 ≈ 1.609
ChallengeHow long to double at continuous rate 5%? (t = ln 2 / 0.05)
Answer: ≈ 13.9 years