I am reading about $D_{KL}$ and I faced these equations which are confusing for me. Can someone explain what $q$ is doing as the index of expectation? $$\log p(x)=\log \int_zp(x,z)=\log \int_z p(x,z) \frac{q(z)}{q(z)}=\log \Big( \mathbb {E}_q \frac{p(x,Z)}{q(z)} \Big)=\mathbb {E}_q[\log p(x,Z)] ...