2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159510We prove that the logarithm of a group-like element in a free algebra coincides with its image by a certain linear map. We use this result and the formula of Le and Murakami for the Knizhnik-Zamolodchikov (KZ) associator $Φ$ to derive a formula for $\log(Φ)$ in terms of MZV's (multiple zeta values).This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/Quantum Algebratext