  In the present paper we study the long-standing problem for the
thermodynamics of magnetized dilaton black holes. For this purpose we construct
an exact solution describing a rotating charged dilaton black hole immersed in
an external magnetic field and discuss its basic properties. We derive a
Smarr-like relation and the thermodynamics first law for these magnetized black
holes. The novelty in the thermodynamics of the magnetized black holes is the
appearance of new terms proportional to the magnetic momentum of the black
holes in the Smarr-like relation and the first law.
