A logarithmic distance of base-\(b\) numbers, where

\(x\) is within \(n\) orders of magnitude of \(y\)

if and only if

\begin{align*} x & < y \cdot b^{\pm n} \\[1ex] y \cdot b^{-n} < x & < y \cdot b^{+n} \\[1ex] b^{-n} < \frac{x}{y} & < b^{+n}. \end{align*}

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• Practice implementation