Well, I'm not sure how order works.

But the main problem here is the ignorance of logx parameter in big O notation, right? 
That is why I suppose, O(x**4*logx**4) is evaluated as O(x**4) because it ignores logx. (I could be wrong here. Please correct me if I am.)

I was only suggesting that O(x**4*logx**4) should not be evaluated to O(x**4). It should not ignore the logx parameter.

Hope I make sense.