In the category of log schemes, it is unclear how to define the blowups for nonstrict
closed immersions. We introduce the notion of divided log spaces. We obtain the
category of divided log spaces by locally inverting log blowups in the category of log
schemes. We show that blowups exist for closed immersions of log smooth divided log
spaces. This is an ingredient of the motivic six-functor formalism for log
schemes.
