  We calculate the Fuglede-Kadison determinant for operators of the form
$\sum_{i=1}^n M_{f_i}L_{g_i}$ where $L_{g_i}$ are unitaries or partial
isometries coming from Borel (partial) isomorphisms $g_i$ on a probability
space which generate an ergodic equivalence relation, and $M_{f_i}$ are
multiplication operators. We obtain formulas for the cases when the relation is
treeable or the $f_i$'s and $g_i$'s satisfy some restrictions.
