For $n\in\mathbb{N}$, prove that $2^n$ can begin with any sequence of digits. Hint: $\log 2$ is irrational number.
Problem
Source: Mathcenter Contest / Oly - Thai Forum 2009 R1 p5 https://artofproblemsolving.com/community/c3196914_mathcenter_contest
Tags: number theory, Digits, power of 2