  We calculate the limiting gap distribution for the fractional parts of log n,
where n runs through all positive integers. By rescaling the sequence, the
proof quickly reduces to an argument used by Barra and Gaspard in the context
of level spacing statistics for quantum graphs. The key ingredient is Weyl
equidistribution of irrational translations on multi-dimensional tori. Our
results extend to logarithms with arbitrary base; we deduce explicit formulas
when the base is transcendental or the r:th root of an integer. If the base is
close to one, the gap distribution is close to the exponential distribution.
