Every time a number doubles (or increases 10×, or 𝑒×, whatever), it moves a constant distance on a log scale because its base-whatever logarithm increases by a constant amount. Hence my expectation of equal distance from 500 to 1000 and 1000 to 2000. I am ignoring 1500 here because it does not form a geometric sequence with any two other numbers so it can’t easily be used for this check.
Every time a number doubles (or increases 10×, or 𝑒×, whatever), it moves a constant distance on a log scale because its base-whatever logarithm increases by a constant amount. Hence my expectation of equal distance from 500 to 1000 and 1000 to 2000. I am ignoring 1500 here because it does not form a geometric sequence with any two other numbers so it can’t easily be used for this check.