How can X-rays penetrate matter that light cannot?

Because of shorter wave lengths that results in more energy than other wavelengths on the electromagnetic spectrum.

They are both part of the electromagnetic spectrum. They are waveforms, as arelight rays, microwaves, and radio waves. X-rays and gamma rays cannot been seen, felt, or heard ... Due to their short wavelength they have more energy to pass through matter than do the other forms of energy in the electromagnetic spectrum.