~/TrinityCore7/src$ grep -inr quest_tracker
server/game/Handlers/QuestHandler.cpp:458: if (sWorld->getBoolConfig(CONFIG_QUEST_ENABLE_QUEST_TRACKER)) // check if Quest Tracker is enabled
There is a quest_tracker db, although I could not find it here: https://trinitycore.atlassian.net/wiki/display/tc/Characters where it should be...
Be sure you have the config enabled.. https://github.com/TrinityCore/TrinityCore/blob/master/src/server/worldserver/worldserver.conf.dist#L997
But, that's where it is stored. no need for a "log file" better to track in a DB.
That what you are asking?
EDIT:
Iv'e only used it on my 3.3.5a servers. I just double checked that it works on the 7.x version.