= Solution
Changing currency or monetary units multiplies amounts by a common constant without changing their generating mechanism. This motivates <scale invariance of decimal significands> of a generic significand distribution.
Multiplication by $c$ adds $\log_{10}c$ to the logarithm, rotating its fractional part. A probability distribution on the unit circle invariant under every rotation must be uniform: equal-length arcs have equal mass, and subdivision fixes that mass to arc length. Uniform fractional logarithms then give <Benford law>. Thus \b[unit or currency invariance motivates uniform logarithmic mantissas]. Restricted ranges, prescribed thresholds and rounding can prevent a particular collection from having this invariance.
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