Exercise 3.2.5
$\star$ Which is asymptotically larger: $\lg(\lg^*n)$ or $\lg^*(\lg{n})$.
The second, because:
$$ \lg^*(\lg{n}) = \lg^*n - 1 > \lg(\lg^*(n)) $$
$\star$ Which is asymptotically larger: $\lg(\lg^*n)$ or $\lg^*(\lg{n})$.
The second, because:
$$ \lg^*(\lg{n}) = \lg^*n - 1 > \lg(\lg^*(n)) $$