I may be wrong but I don’t think your code will work correctly when updating sets: the inserted and deleted tables are what thet are: tables and not rows.
You are logging the changes to one row, not a set.

The following code works for an update trigger.
You can add similar code for delete and insert statements (or you can change this one to cover the three possibilities)

INSERT INTO PriceHistory(ItemId, OldPrice, NewPrice)
SELECT I.ItemId, D.Price, I.Price
FROM INSERTED I INNER JOIN DELETED D ON I.ItemId = D.ItemId
WHERE I.Price != D.Price

Kind regards,

Karel Vandenhove