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We first introduce and study the notion of multi-weighted blow-ups, which is later used to systematically construct an explicit yet efficient algorithm for functorial logarithmic resolution in characteristic zero, in the sense of Hironaka. Specifically, for a singular, reduced closed subscheme $$X$$ of a smooth scheme $$Y$$ over a field of characteristic zero, we resolve the singularities of $$X$$ by taking proper transforms $$X_i \subset Y_i$$ along a sequence of multi-weighted blow-ups $$Y_N \to Y_{N-1} \to \dotsb \to Y_0 = Y$$ which satisfies the following properties: (i) the $$Y_i$$ are smooth Artin stacks with simple normal crossing exceptional loci; (ii) at each step we always blow up the worst singular locus of $$X_i$$, and witness on $$X_{i+1}$$ an immediate improvement in singularities; (iii) and finally, the singular locus of $$X$$ is transformed into a simple normal crossing divisor on $$X_N$$. Comment: Final published version