I tend to get stuck with them more than I care for, and I always measure them on the exterior, just like any other home. Whether their corners are saddle notch, butt and pass or dovetail, it's easy to determine which log sides indicates the "exterior" of the wall you're trying to measure.
As for deciding what the thickness of the log wall is, it too is simple. Measure one of the exposed log ends outside as a start. If a home is very custom (varying log sizes), then it can get sticky, otherwise log diameters are close to uniform enough to just go with measuring 1 or 2 of the exposed ends. If the interior is drywall finished or tongue/groove paneled, then you have to guesstimate that thickness - it generally isn't that thick - less than 1" to maybe 1.5" if there is a styrofoam insulator (99.9% of genuine "log" homes have no exterior wall insulation - so no worries about it.) Take a screwdriver in with you and remove a electrical outlet cover if the interior is finished, if you want to get down to the exact thickness. I've never had to measure the interior of a log home to get a wall distance - not including basements, and sloped upper levels/dormers, of course. And I've probably done close to 50 of them since becoming an appraiser back in the early 90s.
This all goes out the window if the home is simply "log sided" or "half-log/D-log sided", but then again, that means it isn't technically a log home at that point. I've seen half-log siding on manufactured doublewides.
No, there is no formula. Formulas, I find, are flawed anyway. Some wall thicknesses in normal stick-built around here range from .42-.45ft for vinyl and Masonite, to .75-.77ft for brick veneer. This goes against the .50 most guidelines allow. An actual wall thickness is easy to determine on a home that has an attached garage - if you use a tape measure and know how to define a control point from which to measure in the interior vs exterior.
