How to write log in C++?

Try this piece of code:

void __loggi(const TCHAR* t,...)
{
  const TCHAR*  file = __TEXT("c:\\temp\\mylogfile.txt");
  HANDLE        h = ::CreateFile(file,GENERIC_WRITE,0,0,OPEN_ALWAYS,0,0);
  if(INVALID_HANDLE_VALUE!=h)
  {
    unsigned long    w = 0;
    va_list          val;
    TCHAR            f[0x1000];
    int              l;

    va_start(val,t);
    l = _vsntprintf_s(f,sizeof(f)/sizeof(f[0]),_TRUNCATE,t,val);
    va_end(val);
    if(0==SetFilePointer(h,0,0,FILE_END))
    {
      if(sizeof(short)==sizeof(TCHAR))
      {
        unsigned short  unicode = 0xFeFF;
        WriteFile(h,(void*)&unicode,2,&w,0);
      }
    }
    WriteFile(h,(void*)f,l*sizeof(TCHAR),&w,0);
    CloseHandle(h);
  }
}

Example:

void main()
{
  __loggi(__TEXT("hello world\r\n"));
}

Good luck.

MSDN: "The application log contains specific events logged by applications. Applications developers decide which events to monitor."
In your case, you want to write error log while debugging your application. Thus, you have to create some exception handling procedure and output caught errors in file. It does not matter much if you use cerr or clog for this. Any output in file using ostream will be okay. What is important is to how to isolate or catch errors to be logged.
Here is a sample code to create exception handling with output to cerr (console) stream.