We construct a Hennings type logarithmic invariant for restricted quantum sl(2) at a 2p-th root of unity. This quantum group U is not braided, but factorizable. The invariant is defined for a pair: a 3-manifold M and a colored link L inside M. The link L is split into two parts colored by central elements and by trace classes, or elements in the 0 th Hochschild homology of U , respectively. The two main ingredients of our construction are the universal invariant of a string link with values in tensor powers of U , and the modified trace introduced by the third author with his collaborators and computed on tensor powers of the regular representation. Our invariant is a colored extension of the logarithmic invariant constructed by Jun Murakami.