we're the expected value of the log of something to make it into log of expected value that's Jensen's inequality we've seen that in variational auto-encoders see it in many many places in machine learning we just applied Jensen's inequality expected value of the log smaller than log of the expected value and noise brought along we have the expected value of the log is over here whereas the log of the expected value is above and so we have just an equality applied here how about the next step we do this is going to be