iocasq4

2022-01-22

Use the unique factorization for integers theorem and the definition of logarithm to prove that ${\mathrm{log}}_{3}\left(7\right)$ is irrational.

Expert

Use that
${\mathrm{log}}_{3}\left(7\right)=\frac{a}{b}⇔b\mathrm{log}\left(7\right)=a\mathrm{log}\left(3\right)⇔\mathrm{log}\left({7}^{b}\right)=\mathrm{log}\left({3}^{a}\right)⇔{7}^{b}={3}^{a},$