Skyrim: Quest not showing in game log
Based on the UESP article on Forbidden Legend., there are actually three ways to activate the quest without it showing on your quest log:
- Defeat Sigdis in Geirmund's Hall
- Defeat Jyrik in Saarthal
- Defeat Mikrul in Folgunthur
If you simply killed the quest NPC and failed to read the writ of sealing, the quest will be ACTIVE but you will not have a quest log.
In order to get the quest to show up, the trigger will be reading one of the related quest item.