The price depends, among other things, on the log construction technique. Machine-made or manual, hand-hewn side/sides, handcrafted tenons and joints, etc.
An essential decision to make is whether the log structure should be visible on the inside and/or outside.
Personally, I see no need to insulate a new log structure. The most important thing is convection protection, i.e., the structure should be airtight (not watertight).
I believe I saw a new trade magazine about log houses at byggtjänst in Stockholm. Call and ask them.