How to calculate a natural logarithm
- Base e is preselected. Enter the number x (positive). You can type values such as 2.5, 1/3 or 6.02e23.
- Read ln(x) and the check eʸ = x.
- The table also lists log₁₀(x), log₂(x) and eˣ.
About ln and the number e
The natural logarithm ln(x) is the logarithm with base e ≈ 2.718281828, the constant that describes continuous growth. ln(x) answers "for how long must something grow continuously at 100% to reach x times its size?". It turns up everywhere in science and finance: the time to double at a continuous rate r is ln(2) ÷ r (the basis of the "rule of 70"), radioactive half-lives use ln(2), and the decibel and Richter scales and many statistics formulas rely on logarithms.
Key values: ln(1) = 0, ln(e) = 1, ln(2) ≈ 0.6931, ln(10) ≈ 2.3026. To convert to base 10, divide by ln(10): log₁₀(x) = ln(x) ÷ 2.302585. The natural logarithm is undefined for zero and negative numbers. Results are computed in double precision in your browser.
FAQ
What is ln(0)?
It is undefined; ln(x) goes to minus infinity as x approaches 0.
How do I calculate ln on a calculator?
Use the ln key, or log(x) ÷ log(e).
What is ln(2)?
About 0.693147.