What Is an ln Calculator?
An ln calculator computes the natural logarithm of a number — the logarithm to base e, where e ≈ 2.71828. The natural log answers the question "e raised to what power gives this number?" and appears throughout calculus, growth and decay models, finance, and science. Enter a positive number and the calculator returns its natural logarithm, and can also compute the inverse, e^x.
How to Use the Calculator
- Enter a positive number.
- Calculate — see its natural logarithm.
- Optionally compute e^x to reverse the operation.
What the Natural Log Means
If e^y = x, then ln(x) = y. For example, ln(e) = 1 because e¹ = e, and ln(1) = 0 because e⁰ = 1. The natural log is the inverse of the exponential function e^x.
Common ln Values
| x | ln(x) |
|---|---|
| 1 | 0 |
| e ≈ 2.718 | 1 |
| 10 | 2.303 |
| 100 | 4.605 |
Properties of Natural Logs
- ln(ab) = ln(a) + ln(b) — log of a product is the sum of logs.
- ln(a/b) = ln(a) − ln(b) — log of a quotient is the difference.
- ln(aⁿ) = n·ln(a) — exponents become multipliers.
- ln(1) = 0 and ln(e) = 1.
Where the Natural Log Is Used
- Calculus: integrals and derivatives of exponential functions.
- Finance: continuous compounding and growth rates.
- Science: radioactive decay, pH, and population models.
Frequently Asked Questions
What is the natural logarithm?
The natural logarithm, ln, is the logarithm to base e (about 2.718). It is the inverse of the exponential function e^x.
What is the difference between ln and log?
ln is the logarithm base e, while log usually means base 10. Both measure how many times a base is multiplied to reach a number, but with different bases.
What is ln(1)?
ln(1) equals 0, because e raised to the power 0 equals 1.
Can you take ln of a negative number?
No — the natural log is only defined for positive numbers, since e raised to any real power is always positive.
Is this ln calculator free?
Yes — it is completely free, requires no signup, and computes natural logs and e^x.