You should have the exterior caulked completely; ever chink line and every butt joint. If you can see day light that means that water can get in between the logs and will cause rot over time. Use Energy Seal from Perma Chink and it will last for many years. I would also recommend getting a professional to do this. Get some references before hiring anyone. Once a bad caulk job is applied to a log home, it can be very expensive to repair and make right.