https://www.youtube.com/watch?v=1Hqm0dYKUx4
Video states that a corollary of the Rational Root Theorem is that $\left(\frac{a}{b}\right)^n != 2$ for integers $a,b,n$, where $n \gt 1$.
I'm simply looking for a proof by contradiction of this.
I started of by assuming $\left(\frac{a}{b}\right)^n = 2$, but couldn't arrive at a contradiction. (I'm probably very close).
Any ideas?
I got to: $n(\log a - \log b) = \log 2 = 0.30102..$