Base N Logarithm Calculator

Enter any number and any base to instantly compute the logarithm using the change-of-base formula.

Logarithm Inputs

Quick Presets

Result

Enter a number and base, then click Calculate.

Change-of-Base Formula

logb(x) = ln(x) / ln(b) = log10(x) / log10(b)

Any logarithm can be computed as the ratio of two natural (or common) logarithms.

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Summary

Enter any number and any base to instantly compute the logarithm using the change-of-base formula.

How it works

  1. Enter the number (x) you want to find the logarithm of.
  2. Enter the base (b) for your logarithm.
  3. The calculator applies the change-of-base formula: log_b(x) = ln(x) / ln(b).
  4. The result is displayed instantly with high precision.
  5. Use the preset buttons to quickly switch to common bases (2, e, 10).
  6. Copy the result to your clipboard with one click.

Use cases

  • Calculate log base 2 for computer science and information theory problems.
  • Verify change-of-base homework or exam answers.
  • Compute natural logarithms (base e) and common logarithms (base 10).
  • Explore logarithmic relationships in signal processing and decibel calculations.
  • Solve exponential equations by computing logs to arbitrary bases.
  • Check logarithm results from a scientific calculator.
  • Use in finance for compound interest and growth rate calculations.
  • Support data science work involving entropy and information gain.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu