Skyrim Sidelines- The House of Horrors: Reach Out and Smash Someone

Whichever method works on Logrof, untie the man's bindings and he'll inform you that he has other things to do elsewhere- following him won't get you anything special and he thankfully will wind up in Markarth anyways, so just let him be for now.  If nothing else, Molag Bal's influence will operate on him and force him to go to the abandoned home.

Presently, you'll return to Markarth, at which point you can meet Logrof in the abandoned home.  The priest knows the way, quickly running off towards the altar.  He will slow down to let you catch up, so follow him to the passage behind the bookshelf, where he will approach Molag Bal's altar.  The Daedric Prince triggers his trap again, imprisoning Logrof.  The priest is oddly unworried, mostly because he's survived facing Molag once before- but unfortunately for him, he was alone at the time.

The two will argue, but you will hear Molag in your head yet again- granting you the use of the rusty mace and bidding you to beat Logrof with it until the priest gives in.  Unfortunately, you cannot leave until you have completed the task, so take up the mace and begin smacking Logrof through the spaces between the imprisoning spikes.  The man puts up a brave face, refusing to submit (rather loudly) as you beat on him.  In fact, you will wind up beating him all the way to death.

Molag finds this hilarious, particularly for how frail human bodies are, and after a few moments he resurrects Logrof, insisting that the beating will continue until the priest's attitude returns.  It only takes two more hits with the mace before the priest realizes the awful truth- that Molag Bal can and will keep resurrecting him for you to beat to death for as long as the Daedric Prince deems it entertaining.  Giving in, Logrof pledges himself to Molag Bal, vocally forsaking 'the weak and pitiful' Boethiah.  Molag accepts this and deems the pledge worthy...

as long as you kill Logrof again right now.

With Logrof once more dead, Molag Bal speaks to you again, unlocking the full power of the mace and informing you that he will watch you just to see your enemies crushed and killed before you.  Then he finally leaves you alone.

The Abandoned Home is yours to use as you like, though it cannot count as your Home for purposes of the game's records.  If you carry the mace around, guards will comment on it from time to time, and you may get some very dim looks from other Vigilant of Stendarr you run across.  Otherwise, though, your interactions with the Lord of Corruption are over.