Shown above is a photo of one of my many slide rules. This is my favorite, an all-metal Picket Model N4-ES. Many of the scales are arranged in logarithmic basis. Benford's law states that with collections of numbers ranging over multiple magnitudes, there is a tendency for more numbers to begin with low digits than with higher digits. One explanation uses a logarithmic scale as one shown below:
(image credit: https://commons.wikimedia.org/wiki/User:GKFX )
Let this scale represent a collection of data spanning three orders of magnitude. Picking a point along the scale at random, one will has a 30% of landing with a number beginning with 1 and under just under 5% for a number beginning with 9.
Link to prior post on Benford Distribution.
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