On Windows 10, run DISM (Deployment Image Servicing and Management) tool prior to running the SFC (System File Checker).
DISM.exe /Online /Cleanup-image /Restorehealth
If your Windows Update client is already broken, use a Windows side-by-side from a removable media. Then run:
DISM.exe /Online /Cleanup-Image /RestoreHealth /Source:C:\RepairSource\Windows /LimitAccess
The changes can be found here: %WinDir%\Logs\CBS\CBS.log
Or you can export to your TEMP folder by running the following command:
findstr /c:"[SR]" %windir%\Logs\CBS\CBS.log > "C:\TEMP\sfclogs.txt"