Logarithm Calculator

Pick a base — base 10 (common log), base e (natural log, ln), base 2 (binary log), or a custom base — and enter the value. The calculator uses the change-of-base formula log_b(x) = ln(x) / ln(b), so any base works. The result tells you the power to which the base must be raised to get your value.

"log" usually means the common logarithm (base 10), "ln" is the natural logarithm (base e ≈ 2.71828), and log base 2 (the binary logarithm) is common in computer science. They differ only in the base; this tool shows all three at once, plus any custom base you enter.

Logarithms are only defined for values greater than 0, so the log of 0 or a negative number is undefined. The custom base must also be greater than 0 and not equal to 1 (base 1 has no logarithm). When an input breaks these rules the result reads "Undefined".

No. The calculation runs entirely in your browser using the standard Math library. The value and base you enter never leave this page and nothing is uploaded to a server.