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
Les Bases
log₁₀(x) : logarithme décimal. log₁₀(100) = 2 car 10² = 100. ln(x) = logₑ(x) : logarithme naturel (base e ≈ 2,718). log₂(x) : informatique. log₂(1024) = 10 car 2¹⁰ = 1024. Propriétés : log(a×b) = log(a) + log(b). log(aⁿ) = n×log(a).
Applications
Décibels (son). Échelle de Richter (séismes). pH (acidité). Complexité algorithmique (O(log n)). Finance : temps de doublement = ln(2)/ln(1+taux) ≈ 72/taux%.
⚡ 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
Différence log et ln ?▾
log = base 10. ln = base e (2,718...). En mathématiques pures, « log » signifie souvent ln. En sciences, log signifie log₁₀.
À quoi sert le logarithme ?▾
Transformer les multiplications en additions. Analyser la croissance exponentielle. Comprimer de grandes échelles (décibels, Richter).
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