Personally I don't think these new options are what I would want as an alternative to the small digit - the small digit is a shorthand, but as an alternative I wouldn't want another arbitrary format, I'd want the same format used for the powers of ten but extended to multiples.

The behavior I'd want:

• if the power of ten is shown as 0.1, 1, 10 etc (as it is by default): minor labels 0.2, 0.5, 2, 5, 20, 50 etc.
• If the power of ten is 100, 1k, 10k: minor labels 200, 500, 2k, 5k, 20k...
• If the power of ten is 10^2, 10^3, 10^4: minor labels 2x10^2, 5x10^2, 2x10^3, 5x10^3
• If the power of ten is 1e2, 1e3, 1e4: minor labels 2e2, 5e2, 2e3, 5e3...

Basically for all cases except 10^N where you have to put Dx10^N, I'd want the minor labels to simply replace the 1 in the next lower power of ten with the appropriate digit.

While we're at it, another thing people might want is to not show the minor labels at all, just the minor gridlines - so you could setnticks very large and get a lot of gridlines like you see on log-scale graph paper but a manageable number of labels. So for the new attribute perhapsminorloglabels = 'small digit' | 'complete' | 'none'?

Thank you@alexcjohnson for the suggestion.
Please review the revised PR.