If you just want to determine if a pot is audio taper or not, measure the resistance between the wiper and one end with the wiper in the middle. You should read .2-.3 (or .7-.8) of the total resistance for an audio pot.

The theory: :P

The computation is not that easy: If you define the travel going from 0 to 1 (zero volume to full volume), you run into problems because log(0) tends to negative infinity, no matter what the base of the logarithm is.

I derived a formula for that a while ago. The assumptions were:
- R(0) = 0
- R(1) = 1
- R(.5) = 1/sqrt(10) ~ .3162

The last constraint comes from the fact that half volume is achieved with 1/10 of the maximum power, and therefore with 1/sqrt(10) of the maximum amplitude.

I came up with: R(x) = ((sqrt(10)-1)^(2x) - 1)/(10-2sqrt(10)) ,

where x is the travel (0 <= x <= 1).

One can arrive at this result by choosing a logarithmic or exponential law with a couple of unknowns, which are then determined by the boundary conditions above.

All that being said, commercial pots deviate from this characteristic. For example, if you look at the datasheets on the ALPS website, you'll see that they have less than 0.3162 in the middle of the travel for their log pots. I'm not sure why they do that, perhaps it is just a rule of thumb that 1/10 power gives half the volume.
Let the thunder roll and the lightning flash, I'm doing alright for country trash.