If you need to export the System or Application event log from host which is running Windows Server Core you can follow the steps below:

1. Navigate to the host where the Windows Server Core is running
   
   
2. Open PowerShell with elevated permissions
   
   
3. Paste one the following command in the PowerShell console:
   1. System event log

      wevtutil epl System C:\System_Event_Log.evtx

       

   2. Application event log

      wevtutil epl Application C:\Application_Event_Log.evtx

       

   3. Hyper-V VMMS event log

      wevtutil epl Microsoft-Windows-Hyper-V-VMMS-Admin C:\VMMS_Admin_Log.evtx

4. Once completed the commands will export full unfiltered event logs (System or Application) in the root of C:\ drive.