It's impossible to find Logan. After the darkness, Logan chooses to leave Albion remarking, 'Albion will heal better without me', at Sir Walter Beck's memorial. Although, if you miss him, it has been mentioned that:
"The player can find an address from Logan in Bowerstone Industrial, in an alleyway nearby one of the Gnomes. In the voice-over, Logan makes a patriotic yet stern appeal to the citizens of Albion, asking them to ready themselves for war without question. His sentiments seem to be a projection of his own severe sense of duty, summarized in his closing words: "... You will give every ounce of strength, and you will offer your very lives if it (Albion) asks for them. And even then you will never cease to be, for as long as Albion lives, then so will you live too."."
Also, it was said that there is a portrait you can find of him in the Bowerstone Castle gardens, though your dog must be in the high exploration skill level. Too, In the novels, It was mentioned that The Hero of Brightwall did indeed pardon his/her older brother, Logan, although he still left and nothing was ever said about his whereabouts. Sadly, the answer to your question is; there is no possible way to find the former king of Albion anymore, after the final battle against the darkness.
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