We have recently demonstrated high repetition rate tabletop lasers operating at wavelengths as short as 10.9 nm based on collisional transient excitation of ions in plasmas created by laser heating of solid targets. As a further step in the development of these lasers into very high brightness and fully coherent soft x-ray sources, we have demonstrated injection seeding of the amplifiers with high harmonic seed pulses. We report results of an experiment in which a 32.6 nm Ne-like Ti amplifier was used to amplify a seed pulse from the 25th harmonic of Ti:Sapphire into the gain saturation regime. Simultaneous amplification of the 27th harmonic at 30.1 nm was also observed. The seeded soft x-ray laser beam was measured to approach full spatial coherence. We have demonstrated that this scheme is scalable to shorter wavelengths and that is capable of producing extremely bright soft x-ray laser pulse with essentially full coherence.