Logarithm Calculator
Formula
ln(x) = natural logarithm
The natural logarithm (ln) uses base e (≈2.718). Log base 10 is the common logarithm. ln(100) ≈ 4.605, log₁₀(100) = 2.
How to use
- Enter a positive value in the Number field.
- The tool computes both the natural log and log base 10.
- Read the Natural Log (ln) and Log Base 10 results.
Example
Enter 100 in the Number field. The natural log is about 4.605170, and the log base 10 is exactly 2 because 10 squared equals 100.
Frequently Asked Questions
What is ln?
ln is the natural logarithm — the inverse of e^x. ln(e) = 1.
What is log base 10?
log₁₀ answers: '10 to what power equals this number?' log₁₀(100) = 2 because 10² = 100.
What is the difference between ln and log on a calculator?
On most calculators, "ln" means the natural logarithm using base e (about 2.718), while "log" usually means the common logarithm using base 10. Engineering and finance often use base 10, while calculus, statistics, and growth or decay problems favor the natural log. This tool shows both side by side so you do not have to guess which one a formula expects.
How do I find a logarithm with a base other than e or 10?
Use the change-of-base formula: log base b of x equals ln(x) divided by ln(b), or equivalently log10(x) divided by log10(b). For example, log base 2 of 8 equals ln(8) / ln(2), which is about 2.079 / 0.693 = 3, since 2 cubed is 8. Any base works as long as you divide by the log of the base.