Hi,
According to your description, I understand that you want to enable SMTP log for Edge Server.
If I misunderstand your concern, please do not hesitate to let me know.
Attention: do not perform protocol log on an Edge Transport server that has been subscribed to the Exchange organization by using EdgeSync. Instead, make the changes in the Transport service on the Mailbox server. The changes are then replicated to the Edge
Transport server next time EdgeSync synchronization occurs.
We can use Set-SendConnector and Set-ReceiveConnector with ProtocolLoggingLevel parameter to enable or disable protocol log for a send or receive connector, for example:
Set-ReceiveConnector "Connection from Contoso.com" -ProtocolLoggingLevel Verbose
Also, we can modify the path of log location. More details about Protocol logging in Exchange 2013, please refer to:
https://technet.microsoft.com/en-us/library/aa997624(v=exchg.150).aspx
For your reference, the default location of relevant log in Edge Server 2010:
Message tracking log: C:\Program Files\Microsoft\Exchange Server\V14\TransportRoles\Logs\MessageTracking
Connectivity log: C:\Program Files\Microsoft\Exchange Server\V14\TransportRoles\Logs\Connectivity
Send protocol log: C:\Program Files\Microsoft\Exchange Server\V14\TransportRoles\Logs\ProtocolLog\SmtpSend
Receive protocol log: C:\Program Files\Microsoft\Exchange Server\V14\TransportRoles\Logs\ProtocolLog\SmtpReceive
Thanks