/var/log/gdm/:*.log {
    # Append time and date to file
    dateext
    dateformat .%Y_%m_%d-%ss
    sharedscripts
    size 500k
    rotate 4
    missingok
}

/var/log/gdm3/:*.log {
    # Append time and date to file
    dateext
    dateformat .%Y_%m_%d-%ss
    sharedscripts
    size 500k
    rotate 4
    missingok
}