Log calculator.
Use this free log calculator to get fast estimates, compare scenarios, and understand the numbers with clear step-by-step context.
Use the Log Calculator.
Results update automatically as you type. No account is required.
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About the Logarithm Calculator
A logarithm calculator answers the question "to what power must the base be raised to get this number?" Logs are the inverse of exponents and are essential in science, finance, and computing.
How it works
log_b(x) = ln(x) ÷ ln(b), the change-of-base formula. Common bases are 10 (log), e ≈ 2.718 (natural log, ln), and 2 (used in computing). The calculator shows all three.
Reading the result
The headline result is the log in your chosen base, with natural log, log base 10, and log base 2 listed for reference.
Note: Calculations run instantly in your browser and use exact mathematical formulas. For very large numbers, results are shown to standard floating-point precision.
FAQ
What is the difference between log and ln?
"log" usually means base 10, while "ln" is the natural log with base e (≈2.718). Both are logarithms, just different bases.
Why must the number be positive?
Logarithms are only defined for positive numbers, because no power of a positive base produces zero or a negative result.
What is the change-of-base formula?
log_b(x) = ln(x) ÷ ln(b). It lets you compute a log in any base using natural logs, which is how this calculator works.