Each rank of the hunting log is unlocked every 10 levels, for example you get ranks 1-10 after a few quests in, then you can start rank 2 at 10, rank 3 at 20, rank 4 at 30, and rank 5 at 40. Based on your avatar looks like you're only level 36 (correct me if that's wrong) so get four more levels and you can get that next hunting log page!