Funny power of two

Algebra Level 3

What is the power of 10 closest to $\LARGE 2^{(2^{(2^{(2^2)})})}$

(as answer, give the power only)

1 solution

Khushro Shahookar
May 13, 2014

$\large 2^2 = 4$

$\large 2^{(2^2)} = 2^4 = 16$

$\LARGE 2^{(2^{(2^2)})} = 2^{16} = 65536$

$\LARGE 2^{(2^{(2^{(2^2)})})} = 2^{65536}$

$log (2^{65536}) = 65536 \ log (2)$ = 65536 x 0.30103 = 19728.3

$log^{-1} (19728.3)$ = 2X $10^{19728}$

Therefore the answer is 19728, the power of 10