Writing to the standard output stream for another application to read

I'm trying to write to the standard output stream so another application (who has started the game as a process and has redirected it's standard output) can read it. However, it seems that Unity3D applications do not write to the traditional standard output using Console.WriteLine and instead write to a UnityEngine.LogWriter class.

In my other application, I can read some standard output that comes from Unity3D when my simulation launches, but can not read my own output.

Thanks, Kevin