You could say that a log scale is useful only when the variable can be usefully regarded as the exponential of something, and I think you'd be tautologically right. That exponential structure just shows up very often, whether from human sensory perception, or from linear systems math, or from economics, or from many other causes.
I generally prefer log units to linear percentages for anything like a scale factor or a ratio. A lot of stuff comes out cleaner and more symmetric, for example because (1 + 0.10)*(1 - 0.10) isn't equal to one exactly, but exp(0.1)*exp(-0.1) is. The case for that in the university chart seems slightly pedantic but fine to me.
I generally prefer log units to linear percentages for anything like a scale factor or a ratio. A lot of stuff comes out cleaner and more symmetric, for example because (1 + 0.10)*(1 - 0.10) isn't equal to one exactly, but exp(0.1)*exp(-0.1) is. The case for that in the university chart seems slightly pedantic but fine to me.