  This paper incorporates the theory of Hochschild homology into our program on
log motives. We discuss a geometric definition of logarithmic Hochschild
homology of derived pre-log rings and construct an Andr\'e-Quillen type
spectral sequence. The latter degenerates for derived log smooth maps between
discrete pre-log rings. We employ this to show a logarithmic version of the
Hochschild-Kostant-Rosenberg theorem and that logarithmic Hochschild homology
is representable in the category of log motives. Among the applications, we
deduce a generalized residue sequence involving blow-ups of log schemes.
