Prove that if n ∈ Z and log2 n is rational, then log2 n is an integer.
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n = 5. $\displaystyle \log_{2} 5 = 2.3219 ...$. Not an integer.Prove that if $\displaystyle n \in \mathbb{Z}$ and $\displaystyle \log_{2} n$ is rational, then $\displaystyle \log_{2} n$ is an integer.