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Log Base Converter

Convert a logarithm from one base to another using the change of base formula.

Convert a logarithm

Result: —
Same value: —
Uses the change of base rule: log base b of x equals ln x divided by ln b.

How to use the Log Base Converter

  1. Pick the base of your logarithm, or choose a custom base.
  2. Enter the number you are taking the logarithm of.
  3. Read the converted value and the equivalent logs in other bases.

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Frequently Asked Questions

Common questions about the free online log base converter.

Enter the number and its base. The tool applies the change of base formula and shows the result.
Log base b of x equals the log of x in any other base divided by the log of b in that same base.
It is 3, because 10 raised to the power 3 equals 1000.
A natural logarithm uses base e, where e is about 2.71828, and it is written as ln.
Powers of 1 are always 1, so no exponent of 1 can give any other number.
No. Real logarithms are only defined for positive numbers, so the tool asks for a value above 0.
Yes. Alongside the base you choose, it lists the same value in the other common bases.
No. All conversions run locally in your browser and nothing is ever sent anywhere.
Yes. It is completely free and unlimited, with no account needed.

Last updated: October 10, 2026