LiveUpdate Logs

Is it possible to have a LiveUpdate Log History in the log list. This will help to track the list of updates installed on the system through Liveupdate. This can also help to track any recent update has caused any malfunctiong. For example, if a customer is not able to access any particular site after running LiveUpdate, the customer can check if this is happened after a recent LiveUpdate. This will also help to track the patches installed to the product through LiveUpdate.