Substitute, x= 2^s(say), so that s = log2(x)

Then, 2^(2^s) = (2^s)^(2^65520)

or, 2^(2^s) = 2^(s*(2^65520))

or, 2^(s-65520) = s ------------------------(#)

We know that 2^16 = 65536, so that,

s=65536 satisfies both sides of (#).

Consequently;  

log2log2(x) = log2(s) = log2(65536) = 16.

Edited on June 11, 2006, 3:00 pm

Edited on June 11, 2006, 3:13 pm

Posted by K Sengupta on 2006-06-11 14:59:06