Textbook Problem

For each positive real number $u,{\log }_{2}u<u$Use this fact and the result of exercise 21 in Section 11.1 to prove the following: For every integer $n\ge 1$ , if x is any real number with $x>{\left(2n\right)}^{2n}$ then ${\log }_{2}x<x^{1/n}$ .