These logs are needed for the Big Chompy Bird Hunting quest to make Ogre bows as well as Composite ogre bows for Zogre Flesh Eaters. After giving Uglug Nar a relicym's balm during Zogre Flesh Eaters, he will open his store which stocks 100 achey tree logs at a base price of 4 coins. Uglug's store is the best way to obtain Achey logs.