Distance Formula Redux
Prepared 2007-07-24 (149/92544#12) by Bill Claff

The Symbolic Math Showing 'Equivalence' of the Formulas
The conventional formula is d = 0.01 * 10 ^{(x / 40)}
0.01 = 10 ^-2 so d = 10 ^{(x / 40 - 2)}
Rearrange the exponent for d = 10 ^{((x - 80) / 40)}
10 = 2^log₂⁽¹⁰⁾ so d = 2^log₂^{(10) * ((x - 80) / 40)}
Rearrange the exponent for d = 2^{((x - 80) * log}₂^{(10) / 40)}
Note that log₂(10) ~= 3.322 ~= 3.333... = 10 / 3 = 40 / 12
Replace into the exponent to get the formula I claim is correct
d = 2^{((x - 80) / 12)}

Why Favor This Formula?
I have no source and I've never seen an authoritative source for the formula in common use; I believe it was simply derived from the data.
All of the other logarithmic camera metadata is stored as fractional values using a base of 2 and not 10.
So I have no reason to believe that an exception was made for this single case.
In fact, in the assembler language of the firmware, and with limited space, it would make a great deal of sense to leverage any existing firmware code.