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.
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