You can definitely bake the half log. Is the other piece all wood? If so, you can bake that as well. I usually give everything a good rinse in warm water beforehand and then bake for 30 min or so at around 250 (lowest my stove will go) keeping a close eye on it. Let it cool and it should be ready to go.
Thank you cooper dragon I'm going to try this right now! The taller one seems to be all wood I don't see any screws so I'm assuming it's glued together it also has moss on it but it's worth a try .... I will bake them seperate just incase of the glue