The best way I have found is to use a standard compass, the circle drawing type. Push the board against the wall and set the compass to the width of the furthest point from the board. Keep the point and the pencil as dead level as you can, trace the profile of the logs directly on the board.
It's not exact, but it will get you very close. Painter's caulk will get you tight, but I prefer to leave a crack. The logs, in older log homes, will move. Newer engineered logs are a bit more stable. Stuff insulation in before you install the board and seal it up, and it will help deaden noise and air currents from room to room.