The Log file path for WMC Client for ArcGIS has different structure from other Geoportal Clients for ArcGIS Desktop or ArcGIS for INSPIRE desktop extension, C:\ProgramData\ESRI\Geoportal\<ClientName>. The path is 'C:\ProgramData\ESRI\Geoportal\WMC Client' instead of 'C:\ProgramData\ESRI\Geoportal\Logs'.
The log file location has been changed to be consistent with other Geoportal desktop clients for 10.5, the new location is under 'C:\ProgramData\ESRI\Geoportal'.