Change of Base Logarithm Calculator
Enter the values to get the logₐ(x).
Result
How to use
- Enter your values in the fields above.
- Press Calculate to see your result instantly.
- Use the Share button to copy a link to your result.
About this calculator
Most calculators and math libraries only offer base-10 (log) or base-e (ln) functions, yet you often need a logarithm in an arbitrary base a. The change-of-base formula solves this: log_a(x) = log_c(x) / log_c(a), where c can be any convenient base — typically 10 or e — because the ratio of the two common logarithms always equals the logarithm in the original base.
This calculator plugs your value and target base into the formula and returns log_a(x) instantly. It's a staple for algebra and precalculus students working through logarithm rules, computer science learners computing base-2 logarithms for algorithm complexity (like log₂n in binary search), and anyone who needs a log in a base their calculator doesn't natively support.
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