Arora and Barak's online book claims in exercise 6.11 that $NC^1=L$. While the $NC^1\subset L$ direction is relatively straightforward and explained in many other texts, I couldn't prove or find the $L\subset NC^1$ direction anywhere. Since their book is just a draft, I was wondering if their claim was even true?
P.S. I apologize if this is not research-level. Just inform me in the comments and I will take it down if that is the case.