I'm trying to understand what "Log sine sweeps rather than linear sine sweeps were employed to allow verification that non-linear distortion components were virtually absent" actually means.

I understand that a log sine sweep means that the set of frequencies that are tested is itself logarithmic; e.g. you'd check 20Hz, 200Hz, 2KHz, 20KHz instead of 5Hz, 4005Hz, 8005Hz, etc. That makes sense to me. But I don't understand why log sine sweeps would allow you to check for non-linear distortion?