Log translation invariance of log soft gravitational radiation

The gravitational radiation emitted during a classical scattering process is known to exhibit two universal logarithmic terms in its soft frequency expansion. We show that these terms can be written in a way that makes the action of \emph{logarithmic translations} manifest. Invariance under log translations naturally explains a puzzling cancellation in the contribution from outgoing massless particles and leads to a recurrence relation for expected higher-order universal log soft terms.