If you need to view current restore session log, go to the main menu of Veeam Backup for Microsoft Office 365 and select Current log. This will open the corresponding Veeam.Archiver.Shell_<timestamp>.log file.
To open the folder where the management server log files are stored, select Open logs path. Default location of the log files is C:\ProgramData\Veeam\Backup365\Logs.
To open backup proxy server logs, use the same path on the backup proxy server.
To open log files of Veeam Explorer for Microsoft Exchange, use the Open logs path from its main menu. Default location is the C:\ProgramData\Veeam\Backup\ExchangeExplorer\Logs folder on the machine where Veeam Explorer runs.