Quiz on time and space complexity

#1

void pat(){
//executes log (input size) times
for (int i = 2; i <=n; i = pow(i, c)) {
System.out.print("")
}
//Here fun is sqrt or cuberoot or any other constant root
//executes log n times
for (int i = n; i > 1; i = fun(i)) {
System.out.print("")
}
}
a) O(N LogN)
b) O(N^3)
c) O(N^2)
d) LogLog N
Answer is d) LogLog N

I have doubt in this question. How to calculate time complexity in this case?

In this course time complexity lectures are not enough.

#2

Hey @asif_h

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How to calculate the time complexity for this question?
#3

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#4

In case 2 how n ^(1/k^(logk(logn))) comes

#5

Assume looks take m iterations to reach to 1

Then n^(1/k^m)=1
=> log(n) ==k^m
=>Logk(log(n))=m