The only log I've "thrown away" was when I opened an ammo can and the "log" flew out as a cloud of cinders. The victim of a prescribed fire, sadly. The ammo can survived though!
I just wanted to say, some friends and I started geocaching this year as an excuse to hit the forest roads, and we've seen a few caches in bad shape. This thread has provided some great advice, and I'm grateful for that. Thanks!