Resonant inelastic x-ray scattering (RIXS) yields clear evidence of spectroscopic Kondo scales in heavy fermions. In YbInCu4 and YbAgCu4 RIXS probes the Yb2+ component of the hybrid ground state and the temperature dependence of the Yb 4f occupation. We report a sudden valence change at a phase transition in YbInCu4, but a continuous temperature dependence in YbAgCu4, consistent with the predictions of the Anderson impurity model, for a Kondo temperature T(K) = 70 K. These results solve a long-standing controversy and establish RIXS as a quantitative probe of the electronic structure of strongly correlated electron systems.