When an update is executed, the AppLife Update engine writes an execution log to the Local Application Data folder of the system user executing the update.  If you are not using the AppLife Update Windows Service, the logs will be in the current user's local application data folder located here:

XP:  C:\Documents and Settings\[user]\Local Settings\Application Data\Kjs.AppLife.Update

Vista: C:\Users\[user]\AppData\Local\Kjs.AppLife.Update

If you have configured your application to utilize the AppLife Update Windows Service to execute your updates, the service is defaulted to run under the Local System account.  Under the Local System Account, the update engine writes its execution logs here:

XP: C:\Documents and Settings\LocalService\Local Settings\Application Data\Kjs.AppLife.Update

Vista: C:\Windows\System32\config\systemprofile\AppData\Local\Kjs.AppLife.Update