Math
Calculate Logarithms — Any Base
Calculate log base 10, natural log (ln), or any custom base. Shows step-by-step conversion between bases.
In this article
As Bases
log₁₀(100) = 2 pois 10² = 100. ln(x) = logₑ(x) (base e ≈ 2,718). log₂(1024) = 10 pois 2¹⁰ = 1024. Propriedades: log(a×b) = log(a) + log(b). log(aⁿ) = n×log(a).
Aplicações
Decibéis (som). Escala Richter (terremotos). pH (acidez). Complexidade algorítmica O(log n). Finanças: tempo de dobramento = ln(2)/ln(1+taxa) ≈ 72/taxa%.
⚡ CalcWolf Insight
Logarithmic scales are everywhere in daily life: the Richter scale (each whole number = 10x more energy), decibels (every 10 dB = 10x louder), and pH (each unit = 10x more acidic). Understanding logs means understanding these scales intuitively.
Frequently asked questions
Diferença log e ln?▾
log = base 10. ln = base e (2,718...). Em matemática pura, "log" frequentemente significa ln.
Para que serve?▾
Transformar multiplicações em adições. Comprimir escalas grandes. Analisar crescimento exponencial.
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