A.2.5—Logarithmic quantities

A logarithm answers “what power gives this value?” Logarithmic quantities are useful for exponential change and compressed biological scales.

Use log(ab)=log a+log b and log(aᵇ)=b log a where the quantities are defined; keep the base consistent and state it when it matters.

If a population grows tenfold, log₁₀(population) increases by 1; a further tenfold increase adds another 1 rather than multiplying the log by ten.

A log cannot be taken of a non-positive quantity, and equal log intervals represent multiplicative—not additive—changes.