Could you please define $f^* (n) ?$ In Cormen, iterated logarithm function is defined. How would you define $f^* (n)$ here ?

Also, what is the role of $c=2$ here ?

As you have mentioned iterative function here, so you can write:

$f(n) = \frac{n}{\log n}$

Now, here defining $f^2(n)$ as $f(f(n))$ i.e. composition of two functions i.e. $f \circ f$ and not defining $f^2 (n) = (f(n))^2$ and so,

$f^2 (n) = f(f(n)) = f(\frac{n}{\log n}) = \frac{n}{\log n \log \frac{n}{\log n}}$

Similarly, $f^3 (n) = f(f^2(n)) = \frac{n}{\log n \log \frac{n}{\log n}\log \frac{n}{\log n \log \frac{n}{\log n}}} $

$f^i (n) = \frac{n}{g(n) \log \frac{n}{g(n)}}$ for $i \geq 1$

And if you observe, $f^i (n) = \frac{f^{i-1}}{\log f^{i-1}}$ for $i \geq 1$

Also, what is the role of $c=2$ here ?

As you have mentioned iterative function here, so you can write:

$f(n) = \frac{n}{\log n}$

Now, here defining $f^2(n)$ as $f(f(n))$ i.e. composition of two functions i.e. $f \circ f$ and not defining $f^2 (n) = (f(n))^2$ and so,

$f^2 (n) = f(f(n)) = f(\frac{n}{\log n}) = \frac{n}{\log n \log \frac{n}{\log n}}$

Similarly, $f^3 (n) = f(f^2(n)) = \frac{n}{\log n \log \frac{n}{\log n}\log \frac{n}{\log n \log \frac{n}{\log n}}} $

$f^i (n) = \frac{n}{g(n) \log \frac{n}{g(n)}}$ for $i \geq 1$

And if you observe, $f^i (n) = \frac{f^{i-1}}{\log f^{i-1}}$ for $i \geq 1$