  In this paper we discuss log blow-up's, introduced by Kazuya Kato, and define
the concept of log modifications. Using this concept we prove that any morphism
f: X ---> Y of locally noetherian fs log schemes with underlying structures of
f and Y quasi-compact can be modified to an exact morphism, and moreover to an
integral morphism. By a well-known fact on the underlying structure of an
integral morphism this result can be considered as a weak log-version of
flattening theorem by Raynaud and Gruson.
