[rcme]

> piecewise linear vs. frequency on a log-log Bode plot. It has no similarly useful structure on a linear plot.

log-log graphs are not the same as a log graph. A log-log graph is useful for turning monomials into lines, which is exactly what a Bode plot is. But this is a good point. Maybe "exponential function" is the wrong terminology. "Function with an exponent" is more apt.

> stock price charts are sometimes logarithmic.

Stock price charts are logarithmic when the movement of a stock is exponential over the time frame being looked at. Stock prices, in general, are kind of related to perception as well. A $4 stock that moves +/- $2 is perceived very differently than a $100 stock that moves +/- $2. The perception of a price delta is relative to the current price, not the absolute dollar amount of the movement. This is why stock prices exhibit compound returns, which is of course an exponential function.

[lathyrus_long]

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.