Sure it is possible to take A/D readings of the log taper potentiometer at say 28 different positions (i.e. every 10 degrees of rotation from end to end of a 270 degree pot) and use these readings to build a lookup table that translates to a linear equivalent resistance. You would do this as a calibration step. At run time you use the actual A/D readings as an index to the table to lookup what the corresponding linear taper resistance would have been. The actual A/D reading would be used in a "divide by table length" to get the table index. The remainder of the divide algorithm would be used to interpolate between the computed index and the next entry in the table to maximize your resolution. This technique ends up normally being a linear interpolation to keep the math simple.

There are two issues with this technique though. One is that the the sensitivity to position changes of the potentiometer is much greater on one end of the range versus the other. The other problem is the need for the calibration step. It takes a lot of steps for linear interpolation to give a good approximation of the characteristic curve of the log taper pot. You may also find that there is enough variation from unit to unit of the pots that the calibration step may be necessary for each unit. On the other hand selection of a better quality component may end up being repeatable enough so as to only need to be calibrated once and used from unit to unit.

In the end I believe that you shouldn't do this at all. Either buy the proper linear taper potentiometer in the first place OR take a look at your application and you may find that the log curve behavior of the component fits well with what the resistance reading is actually used for. Human perceptions of some properties of such as volume, tone or speed may work very well with a log behavior component (after all there is a reason they were invented in the first place).

Michael Karas