Logarithm Calculator
Compute log base 10, natural log (ln), log base 2, or a logarithm in any positive base.
Reviewed by the WorldCalcs team · Methodology · Last reviewed: June 2026
Result
3
What is a logarithm?
A logarithm answers the question: what power must I raise the base to in order to get this number? If b to the power y equals x, then log_b(x) = y. For example, because 10 to the power 3 equals 1000, log base 10 of 1000 is 3. The base-10 logarithm (written log) and the natural logarithm (written ln, base e which is about 2.71828) are the most common, with base 2 widely used in computing. Logarithms turn multiplication into addition, which is why they appear in sound (decibels), earthquakes (the Richter scale), acidity (pH), and models of growth and decay.
How it's calculated
Any logarithm can be found from natural logs using the change-of-base formula: log_b(x) = ln(x) / ln(b). This is how a calculator evaluates a base it does not have a dedicated button for. The base must be positive and not equal to 1, and you can only take the logarithm of a positive number.
Example
To find log base 2 of 8: ln(8) is about 2.079442 and ln(2) is about 0.693147, so log₂(8) = 2.079442 / 0.693147 = 3. That matches the fact that 2 to the power 3 equals 8.
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Results are estimates and may contain errors — for general information only, not professional advice. Always verify before relying on them. Disclaimer
How to use
Enter the number x and the base. Use the quick buttons for log (base 10), ln (base e) or log base 2, or type any positive base other than 1.
The result is computed with the change-of-base formula: log_b(x) = ln(x) / ln(b).