---
title: "Logarithm Calculator — log, ln, log₂, Any Base"
description: "Calculate log₁₀, natural log (ln), log₂, and any custom base logarithm simultaneously. Shows change-of-base formula and verification. Free."
url: "https://worldcalculators.org/calculators/logarithm/"
canonical: "https://worldcalculators.org/calculators/logarithm/"
---

# Logarithm Calculator

Calculate log₁₀, natural log (ln), log₂, and any custom base logarithm simultaneously. Shows change-of-base formula and verification. Free.

## Quick answer

log_b(x) = y means b^y = x. log (base 10) : log(1000) = 3. ln (base e) : ln(e) = 1. log₂ : log₂(8) = 3. Change-of-base: log_b(x) = ln(x)/ln(b).

## Frequently Asked Questions

On most scientific calculators (TI-84, Casio fx), the "log" button is log₁₀. The "ln" button is the natural logarithm (base e). However, in European pure maths textbooks, "log" often means ln.
pH = −log₁₀[H⁺], where [H⁺] is the hydrogen ion concentration in mol/L. pH 7 is neutral ([H⁺] = 10⁻⁷). Each pH unit is a 10× change in acidity — a pH scale used identically worldwide.

Source: https://worldcalculators.org/calculators/logarithm/
Markdown mirror of the HTML page. Prefer this URL for RAG; the interactive calculator still lives on the HTML page.