The article is really badly flawed. It does not even touch the reason why we use Big-O notation in the first place. That is to avoid clutter like constant factors or the basis of logratihms.

If it would than such mistakes as in the example for binary search "a data set containing 10 items takes one second to complete, a data set containing 100 items takes two seconds, and a data set containing 1000 items will take three seconds."

would not occur.

Also a logarithm does NOT have a "curve that PEAKS [my emphasis] at the beginning and slowly flattens out as the size".