Time-resolved x-ray absorption spectroscopy (TR-XAS) has so far practically been limited to large-scale facilities, to subpicosecond temporal resolution, and to the condensed phase. We report the realization of TR-XAS with a temporal resolution in the low femtosecond range by developing a tabletop high-harmonic source reaching up to 350 electron volts, thus partially covering the spectral region of 280 to 530 electron volts, where water is transmissive. We used this source to follow previously unexamined light-induced chemical reactions in the lowest electronic states of isolated CF4+ and SF6+ molecules in the gas phase. By probing element-specific core-to-valence transitions at the carbon K-edge or the sulfur L-edges, we characterized their reaction paths and observed the effect of symmetry breaking through the splitting of absorption bands and Rydberg-valence mixing induced by the geometry changes.