  We prove criteria for a presheaf on logarithmic schemes to be a sheaf in the
full logarithmic \'etale topology and describe several situations where the
structure sheaf and logarithmic structure are logarithmic \'etale sheaves. We
deduce that the logarithmic Picard group is a stack in the full logarithmic
\'etale topology on logarithmic schemes whose structure sheaves satisfy
logarithmic \'etale descent.
