All 3 logs can be found past the Right exit of the Merchant Camp. They are each in a zone accompanied by a cutscene (Meeting the Hunter, Meeting the Sick Man and finding the strange house.). They're just lying on the floor around these spots and need to be interacted with. If you've found those then you just need the Carpenter's Tools which are in the Slime Nest. That can be found by going Up from the Rest Spot map.
Hope that helps!