Matemática

Logarithm Calculator

Value (x)

Base

🌐

Detailed Guide Coming Soon

We're working on a comprehensive educational guide for the Logarithm Calculator in your language. The content below is shown in English.

O que é Logarithm Calculator?

▾

A logarithm calculator computes log base 10, natural log (ln), log base 2, and any other base. Logarithms are the inverse of exponentiation.

PrimeCalcPro provides professional-grade tools trusted by businesses and academics.

Fórmula

▾

f(x)log_b(x) = y means b^y = x; Change of base: log_b(x) = log_10(x) / log_10(b)

Legenda de variáveis

▾

Símbolo	Nome	Unidade	Descrição
x	Number	—	—
b	Base	—	Usually 10, e, or 2
y	Logarithm result	—	—

Como Logarithm Calculator

▾

1logₐ(x) = y means aʸ = x
2log₁₀(x): common logarithm
3ln(x): natural log, base e ≈ 2.71828
4Change of base: logₐ(x) = ln(x)/ln(a)

Exemplos resolvidos

▾

Exemplo 1

Dado:log₁₀(1000)

Resultado:3 (because 10³ = 1000)

Exemplo 2

Dado:ln(e²)

Resultado:2

Aplicações práticas

▾

🏗️

Scientific and engineering calculations

🔬

Earthquake magnitude (Richter scale)

📊

Sound intensity (decibels)

🏥

pH calculations in chemistry

Logarithm Properties

▾

Property	Formula
Product rule	log(ab) = log(a) + log(b)
Quotient rule	log(a/b) = log(a) − log(b)
Power rule	log(aⁿ) = n×log(a)
Change of base	logₐ(x) = log(x)/log(a)
log(1)	Always = 0, any base

Perguntas frequentes

▾

What's the difference between log, ln, and log₁₀?

log (no base) = log₁₀. ln = natural log (base e ≈ 2.718). log₂ = binary logarithm.

When do I use logarithms?

Solving exponential equations, measuring scales (pH, Richter, decibels), growth/decay rates.

Why is log₁₀ of 1000 equal to 3?

10³ = 1000, so log₁₀(1000) = 3. Logarithm is the inverse of exponentiation.

Referências

›Logarithms — Khan Academy

Comparar com

⇄

Logarithms vs Exponents

Mathematically verified

Reviewed October 2026

Our methodology

Receba dicas semanais de matemática

Junte-se aos assinantes do 12.000 + que recebem dicas de calculadora todas as semanas.

🔒

100% Grátis

Sem registo

✓

Preciso

Fórmulas verificadas

⚡

Instantâneo

Resultados imediatos

📱

Compatível com móvel

Todos os dispositivos

Logarithm Calculator