Hey @nothatcreative5!

The identity $\ln x \leq x - 1$ holds for all $x > 0$. Multiplying this with $-1$, we have $- \ln x \geq 1 - x$ or $\ln \frac{1}{x} \geq 1 - x$, if you want. This is then applied in the first line of eq. 4. But I just see that there is an error: $p(x)$ and $q(x)$ should be reversed in the fraction on the right-hand side of the first line of eq. 4. This will be corrected.

Cheers, Joram.

The error has been corrected.