  Observing that the logarithm of a product of two elliptic operators differs
from the sum of the logarithms by a finite sum of operator brackets, we infer
that regularised traces of this difference are local as finite sums of
noncommutative residues. From an explicit local formula for such regularised
traces, we derive an explicit local formula for the multiplicative anomaly of
zeta-determinants which sheds light on its locality and yields back previously
known results.
