vittorecostao1

2022-06-21

Show that ${\mathrm{log}}_{2}(k)$ is an irrational number if $k$ is an odd integer greater than $1$.

Braylon Perez

Beginner2022-06-22Added 34 answers

${2}^{(a/b)}=k\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}{2}^{a}={k}^{b}.$

But ${2}^{a}$ is even and ${k}^{b}$ is odd.

But ${2}^{a}$ is even and ${k}^{b}$ is odd.