Log Calculator

Calculate the logarithm of a number in any base, plus ln, log₁₀, and log₂.

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  • ⚡ Converted in your browser
  • ✅ No account required

Log Calculator: The Complete Guide

Compute a logarithm in any base. Enter a value and a base to get the logarithm, and see the natural log (ln), common log (base 10), and binary log (base 2) alongside.

Who the Log Calculator is for

Students and engineers computing logarithms for math, science, and information theory.

How to use the Log Calculator

  1. Type your values into the fields above — pick your currency or units where the calculator offers them.
  2. Results update automatically as you type; there's no submit button and nothing is sent to a server.
  3. Adjust any input to compare scenarios, then copy the result with a single click.

How it works

log base b of x = ln(x) ÷ ln(b), using the change-of-base rule. The calculator also reports ln (base e), log₁₀, and log₂ for the same value.

Features

  • Logarithm in any base
  • ln, log₁₀ and log₂
  • Change-of-base rule
  • Instant result

What a logarithm is

A logarithm answers 'to what power must the base be raised to get this value?' — the inverse of an exponent. Base 10 (common log) suits orders of magnitude, base e (natural log) appears in growth and calculus, and base 2 is used in computing and information theory.

Frequently Asked Questions

What's the change-of-base rule?

log base b of x equals ln(x) ÷ ln(b) (or any common base divided the same way), which lets you compute a log in any base from natural logs.

Why can't I take the log of zero or a negative?

Logarithms are only defined for positive numbers, so the calculator requires a value greater than zero.

Is this calculator free and private?

Yes. It's completely free with no signup, and every calculation runs locally in your browser, so your numbers never leave your device.