A recent article by Alexopoulos and Leontsinis presented empirical evidencethat the first digits of the distances to galaxies are a reasonably good fit tothe probabilities predicted by Benford's law, the well known logarithmicstatistical distribution of significant digits. The purpose of the presentarticle is to give a theoretical explanation, based on Hubble's law andmathematical properties of Benford's law, why galaxy distances might beexpected to follow Benford's law. The new galaxy-distance law derived here,which is robust with respect to change of scale and base, to additive andmultiplicative computational or observational errors, and to variability of theHubble constant in both time and space, predicts that conformity to Benford'slaw will improve as more data on distances to galaxies becomes available.Conversely, with the logical derivation of this law presented here, the recentempirical observations may be viewed as independent evidence of the validity ofHubble's law.
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