An experiment shows that equations of state of solid matter at pressure $P=\phantom{\rule{0ex}{0ex}}$10\char21{}50 Mbar can be studied by using lasers with pulse energy $E\ensuremath{\approx}100\mathrm{J}$. Laser beams smoothed by phase-zone plates produced high quality, planar shock waves in two-step, two-material targets, allowing simultaneous measurements of the shock velocities in the two materials. By the use of the impedance-matching technique, the relative consistency of the equations of state of these materials can be tested, or a relative equation of state data can be measured. Pressures higher than 35 Mbar were achieved in gold.