Expectation-maximization works to improve Q(\boldsymbol\theta|\boldsymbol\theta^{(t)}) rather than directly improving \log p(\mathbf{X}|\boldsymbol\theta).
We take the expectation over possible values of the unknown data \mathbf{Z} under the current parameter estimate \theta^{(t)} by multiplying both sides by p(\mathbf{Z}|\mathbf{X},\boldsymbol\theta^{(t)}) and summing (or integrating) over \mathbf{Z}.