Calculadora Logarítmica Online Grátis
Calculate log base 2, 10, e, and any custom base with step-by-step solution
The Logarithm Calculator computes logarithms for any base — including base 2 (binary log), base 10 (common log), base e (natural log), and any custom base you specify. It shows the step-by-step solution using the change-of-base formula where needed. Scientists, engineers, and computer science students use logarithms to work with exponential growth, decibels, pH, and information theory.
Frequently Asked Questions
Sobre Esta Calculadora
Logarithms answer the question: "to what power must the base be raised to produce this number?" The three most common logarithms are log₁₀ (used in chemistry, acoustics, and earthquake measurements), ln (natural log, used in calculus and finance), and log₂ (used in computer science and information theory).
The change-of-base formula, log_b(x) = log(x)/log(b), allows any logarithm to be computed using a calculator that only has log₁₀ or ln. This calculator applies that formula automatically for custom bases, showing the intermediate values.
Logarithms appear in decibel calculations (dB = 10·log₁₀(P₂/P₁)), pH measurements (pH = −log₁₀[H⁺]), the Richter scale, population growth models, mortgage amortization, and Shannon entropy in information theory. Understanding logarithms is essential for any quantitative field.
Uma calculadora poderosa nas resoluções das suas bases complexas com resoluções demonstradas via fórmulas em detalhes para você achar qual será seu resultado no cálculo exponencial.
Exemplo Resolvido
Calculating log base 5 of 125
Entradas:
- Base: 5
- Number: 125
Passo a Passo:
- We want to find x such that 5ˣ = 125
- Recognize 125 = 5³, so x = 3
- Alternatively, using change-of-base formula: log₅(125) = log(125)/log(5)
- log(125) ≈ 2.09691, log(5) ≈ 0.69897
- 2.09691 ÷ 0.69897 = 3.0000