Where were the logarithmic karma system used?

It was a system that used VBulletin, which includes such a module. I have seen similar features available in other similar systems that I have made use of at various times.

The stability could be a problem in the moderately unlikely event that the core group is going sour and new members have a better grasp. I grant that it's more likely to have a lot of new members who don't understand the core values of the group.

True, and unfortunately most systems short of an AI with the 'correct' values will be vulnerable to human stupidity.

I don't think it would be a problem to have a system which gives both the number and total karma-weight of votes.

No particular problem, but probably not necessary just yet!