We measured the low energy excitation spectrum of alpha'-NaV2O5 across its charge ordering and crystallographic phase transition with resonant inelastic x-ray scattering (RIXS) at the V L-3 edge. Exploiting the polarization dependence of the RIXS signal and the high resolution of the data, we reveal the excitation across the insulating gap at 1 eV and identify the excitations from occupied 3d(xy) bonding orbitals to unoccupied bonding 3d(xy) and 3d(yz)/3d(xz) orbitals. Furthermore we observe a progressive change of the electronic structure of alpha'-NaV2O5 induced by soft x-ray irradiation, with the appearance of features characteristic of sodium deficient NaxV2O5 (x < 1).