Accidentally shutdown system while Bitcoin Core client was synchronizing
giving an error as ' fatal error please see error log' ... what is the solution to this problem.


Step one is to do as it suggests. The location of the error log depends on the platform (Windows probably %APPDATA%\bitcoin, Linux probably ~/.bitcoin)

If all else fails, just install some wallet software elsewhere and re-import the private key you carefully backed up for just this sort of situation.