  In the present paper, we determine the algebraic relations among the
tractable coordinates of logarithms of Anderson $t$-modules constructed by
taking the tensor product of Drinfeld modules of rank $r$ defined over the
algebraic closure of the rational function field and their $(r-1)$-st exterior
powers with the Carlitz tensor powers. Our results, in the case of the tensor
powers of the Carlitz module, generalize the work of Chang and Yu on the
algebraic independence of polylogarithms.
