The natural logarithm is the logarithm calculus loves: its derivative is 1/x. It appears in continuous growth and decay, half-lives, compound interest, entropy and the time constant of circuits.
How to use the Natural Log Calculator
- Number x
- Every result field is editable: type into ln x and Number x plus every other field update to match.
Results update as you type, and everything is calculated in your browser.
How it works
Enter x, or type a value into the ln x field to get x = e^(value).
What each result means
- ln x = ln([Number x])
- log₁₀ x = ln([Number x])÷ln(10)
- log₂ x = ln([Number x])÷ln(2)
Example values
How the main result changes when Number x changes and everything else stays at the example values above:
| Number x | ln x |
|---|---|
| 5 | 1.6094 |
| 7.5 | 2.0149 |
| 10 | 2.3026 |
| 12.5 | 2.5257 |
| 15 | 2.7081 |
| 20 | 2.9957 |
Formula
ln x = log_e x, e^(ln x) = x, e ≈ 2.718281828
Worked example
Inputs — Number x: 10.
Results — ln x = 2.302585092994; log₁₀ x = 1; log₂ x = 3.321928094887.
Key terms
- e
- Euler's number, ≈ 2.718281828.
Frequently asked questions
What is ln e?
1.
What is ln 0?
Undefined – ln x goes to −∞ as x approaches 0.
How do I convert ln to log?
log₁₀ x = ln x / ln 10 ≈ ln x / 2.302585.
Why is it called "natural"?
It arises naturally from continuous growth and from the integral of 1/x.