We present a study of the bonding of formate (HCOO) and acetate (CH3COO) chemisorbed on Cu(110) using core level spectroscopies in combination with theoretical calculations. For the first time, we apply x-ray emission spectroscopy (XES) to these systems. When XES is used in conjunction with x-ray absorption spectroscopy (XAS) and ab initio calculations, new information about the electronic interaction in the adsorbate-substrate system is provided. In particular, we have used the azimuthal orientation of the COO-surface bond on the (110) surface, to make a complete partition into x, y, and z orbital contributions. The surface bond is found to be predominantly ionic. For the case of adsorbed formate, the covalent bonding is dominated by 6a(1)/7a(1), (sigma)-type, frontier orbitals, interacting with the Cu valence band. The resulting hybrid orbitals form a distribution of states that cross the Fermi level. The contribution from adsorbate pi-type orbitals is small. The chemical bond formation of adsorbed acetate is very similar to that of formate. In addition, states with metal character have been identified for the outermost CH3-group of acetate. These are delocalized states of mainly local sigma-character. The spectral features due to states of local pi-character in the adsorbed acetate are well described within the framework of hyperconjugation.