Dynamic tree connectivity paper

Im reading this paper currently, “Near optimal fully dynamic graph connectivity” by Thorup.
I have a couple hazy points in this paper and I’ll be grateful if someone can clarify them. I’ll add the hazy points as i go through the paper.
The first one is, on page “346” (the paper has only 10ish pages, idk how its numbered) the last paragraph of “local search trees”: “Now, from … … time O(log n)”.
How did this come about? Am i missing something obvious??