Confusion regarding equations (5) and (6)

[Kiwifed0r]

Hi!

I have a question regarding equations (5) and (6). If I understand it correctly, both cases, i.e., cross entropy and binary cross entropy, use the same probability distribution $q(y|x)$. And the two equations are equivalent and result in the same loss. Is that correct?

In all my tests, I get the same value for the left part of both equations. But I'm confused how the right parts are equivalent.