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Dayo Ogundipe edited begin_itemize_item_textbf_Show__.tex
over 8 years ago
Commit id: ce53ee5d41bf04309564ded9ed8c2fe6fc1c5dd3
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$\therefore log_2(3)$ is not a rational number. Proof by contradiction.
\item Show that $\log_{\sqrt{2}}(3)$ is not a rational number
Assume that $\log_\sqrt{2} (3) = \frac{p}{q}$ where p, q are integers.
\[\sqrt{2}^{\log_{2} (3)} = 3 \]
\[ \sqrt{2}^\frac{p}{q} = 3 \]
\end{itemize}