Logarithm Base Converter

Convert logarithms between bases. Free online log base converter with change of base formula.

The Logarithm Base Converter transforms logarithms from one base to another using the change of base formula. Whether you need to convert between natural log (ln), common log (log₁₀), or any other base, this tool provides instant conversions. Essential for computer science (log₂), mathematics, and scientific calculations.

Common use cases

  • Computer science complexity analysis
  • Information theory calculations
  • Scientific data conversion
  • Calculator compatibility
  • Mathematical proofs

How to use

  1. Enter the original logarithm base
  2. Enter the value (argument) of the log
  3. Enter the target base
  4. Click convert for the result
  5. View the change of base formula

FAQ

What is the change of base formula?

logₐ(x) = logᵦ(x) / logᵦ(a) for any base b. Usually b = 10 or e.

What are common log bases?

Base 10 (common log), base e ≈ 2.718 (natural log), base 2 (binary log).

Why is log₂ important in computing?

Computers use binary, so log₂ appears in complexity analysis (O(log n) typically means log₂).

How do I use my calculator for any base?

Use the change of base formula with log₁₀ or ln: logₐ(x) = log(x)/log(a).