Log Calculator · Practical guide
Natural Log Calculator (ln)
Compute the natural logarithm of any positive number, with the inverse e^x shown so you can verify the result.
At a glance
What Is the Natural Logarithm?
The natural logarithm ln(x) uses base e (about 2.71828). It answers: "e raised to what power equals x?" The most useful fact to remember: ln(10) = 2.302585. Check it with the inverse — e^2.302585 = 10. Above, check "Use base e" and enter your number; the result row, the inverse, and the formula all appear together.
Interactive tool
Log Calculator
Enter your own values, then compare the result with the examples below.
Results
Natural Log Values to Know
| x | ln(x) |
|---|---|
| e (2.71828) | 1 |
| 10 | 2.302585 |
| 20 | 2.995732 |
| 100 | 4.605170 |
| 0.5 | -0.693147 |
| 1 | 0 |
When to Use ln Instead of log
Use the natural log for anything involving continuous growth or decay: compound interest solved for time, half-life problems, and exponential models in science and statistics. Use common log (base 10) for orders of magnitude like pH or decibels. This calculator always shows both — the ln row and the log10 row — no matter which base you select.
The Inverse of ln
The inverse of the natural log is the exponential function: if ln(x) = y, then e^y = x. For example, ln(5) = 1.609438, and e^1.609438 = 5. The calculator displays this inverse automatically, so you can confirm every result round-trips back to your original number.
Frequently Asked Questions
What is the difference between ln and log?
ln is the natural logarithm with base e (about 2.718). Written alone, log usually means base 10, though some fields use it for base 2.
What is ln of e?
ln(e) = 1, because e raised to the power 1 equals e.
Can you take the natural log of a negative number?
No, not in real numbers. ln(x) is defined only for x greater than 0, which is why the calculator asks for a positive number.
What is the inverse of ln?
The inverse is e^x. If ln(x) = y, then e^y = x, and the calculator shows this inverse for every result.