If you live in a log home before you start your chinking make sure you have filled any gaps or checks in the logs with foam backer rod. This will help seal out moisture and will also save on the amount of caulking material needed.
On our place the previous owner used expanding foam to fill in most of the checks and after only a couple years you can see the foam braking down and allowing the caulking to settle into the cracks. If done like the picture below with foam backer rod your chinking job will last many years longer compared to other methods.
It also adds insulation value and helps to combat cold air from following the cracks and infiltrating the home. I have also found many other uses for this foam backer rod such as filling in gaps along window frames, filling cement cracks before filling with mortar and so on. I always try to have a supply of various diameters on hand as it is relatively inexpensive and can be used on so many different projects that it seems to never go to waste.
Hope this gives you a better solution then resorting to the expanding foam and makes your repairs last that much longer.