To generate a log file for a scan, open the scan settings and check the Generate report file, avastUI > Security > Antivirus > Scan Now and select the scan, click More options, Settings, Report file.
You will see an * asterisk in the File name filed, this means the report file will have the same name as the scan name and will be located in the C:\Documents and Settings\All Users\Application Data\AVAST Software\Avast\report folder (XP location) C:\ProgramData\AVAST Software\Avast\report folder (Vista, win7)