Logarithms convert multiplication to addition. Other laws: log(x/y) = log(x) - log(y), log(xⁿ) = n×log(x).
Earthquake magnitude — Richter scale: each unit is 10× more energy (logarithmic).
Sound decibels — dB = 10×log(I/I₀); logarithmic perception of loudness.
pH scale — pH = -log[H⁺]; each unit is 10× change in acidity.
Stellar magnitude — Apparent magnitude is logarithmic; 5 units = 100× brightness difference.
Data compression — Information theory uses log₂ for bits.
Algorithm complexity — O(log n) means doubling input adds one step.
Radioactive dating — Age = (1/λ)×ln(N₀/N); solving exponential decay.
Music intervals — Octaves are logarithmic; each doubles frequency.
Population growth — Doubling time = ln(2)/r.
Slide rules — Historical calculators used log scales for multiplication.
No community explanations yet. Be the first to share yours!
to write your own explanation
to share your insights
No insights yet. Be the first to share!
With Pro, you get AI explanations that connect formulas to real-world applications.
Add to home screen for quick access