Suppose K is a totally real number field and that O_K^* is the group of units of the integers of K. In this talk I will show how if one assumes Schanuel's conjecture about logarithms of algebraic numbers, one can determine the zeta function of K from the isometry class of the rational vector space spanned by the image of the units of K under the usual log map into a Euclidean space. This is joint work with C. Rajan.