We use exhaust fans to control dust.
The worst thing about log homes is how the saw dust keeps coming back for years. This can be avoided. It all begins with how clean logs are prepared during the original staining of new log home finishing.
Regardless of the look you are going for (hand hewn, draw knife, turned logs or manufactured house logs), my log home preparation and methods leaves log walls so naturally smooth you can use a feather duster to clean your home after its all done.