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
Grundlagen
log10(100) = 2 (10^2 = 100). ln(x) = log_e(x) (e ≈ 2,718). log2(1024) = 10. Regeln: log(a×b) = log(a)+log(b). log(a^n) = n×log(a).
Anwendungen
Dezibel (Lautstaerke). Richter-Skala. pH-Wert. Algorithmische Komplexitaet O(log n). Verdopplungszeit = ln(2)/ln(1+Rate) ≈ 72/Rate%.
⚡ 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
Unterschied log und ln?▾
log = Basis 10. ln = Basis e. In Mathematik/Physik bedeutet log oft ln.
Wofuer braucht man das?▾
Multiplikation in Addition verwandeln. Grosse Skalen komprimieren. Wachstum analysieren.
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