We describe the space of deformations of a pair complex manifold + log symplectic form on it, under the assumption that the polar divisor of the log symplectic form we start with has normal crossings singularities. I will start the talk by (giving the necessary definitions and) explaining how to calculate the relevant deformation complex, i.e. the Poisson cohomology. Then I will discuss the L-infinity structure that the Schouten bracket induces on the deformation complex, and what implication this L-infinity structure has about the neighborhood in the given moduli space. I will illustrate usefulness of our technique by constructing new examples of log symplectic forms on the complex projective space CP^4. This is joint work with Brent Pym and Travis Schedler.