The code in Console.cpp's addMessage() overload that operates on a ScriptCallStack suggests that console message like
console.log("x equals", x, "right now")
is only passed to the web inspector and the stdout.
I think it should be passed to the ChromeClient, too, to allow embedding applications to fully catch the output of the Console API.
I have provided a fix to this issue. See bug 26083.
*** This bug has been marked as a duplicate of bug 26083 ***