Again with the twos

Algebra Level 4

If $x$ is a real number that satisfies the following equation:

$\large 2^{2^{x}} + 4^{2^{x}} =56$

So what is the value of $2^{2^{2^{x}}}$ ?

256 128 512 64 32

1 solution

Hana Wehbi
Mar 8, 2017

Let $u = 2^{2^{x}} \implies u+ u^2= 56$ then $u= 7$ . The desired answer is $2^7= 128$