Problem:
If log2​(log2​(log2​(x)))=2, then how many digits are in the base-ten representation for x?
Answer Choices:
A. 5
B. 7
C. 9
D. 11
E. 13
Solution:
Since
log2​(log2​(log2​(x)))=2​⟺log2​(log2​(x))=22=4,⟺log2​(x)=24=16⟺x=216=26⋅210≈64⋅1000,​
it follows that x has 5 base-ten digits.