Монгол Бодлогын Сан

Заавар: $p$ суурьт шилжүүл.

Бодолт: \begin{align*} \log_{\frac{\sqrt{q}}{p}}{\dfrac{\sqrt[3]{q}}{\sqrt{p}}}&=\dfrac{\log_p{\frac{\sqrt[3]{q}}{\sqrt{p}}}}{\log_p\frac{\sqrt{q}}{p}}=\dfrac{\log_p\sqrt[3]{q}-\log_p\sqrt{p}}{\log_p\sqrt{q}-\log_pp}\\ &=\dfrac{\frac13\log_pq-\frac12}{\frac12\log_pq-1}=\dfrac{\frac{\sqrt{3}}{3}-\frac12}{\frac{\sqrt{3}}{2}-1}\\ &=\dfrac{2\sqrt3-3}{3(\sqrt{3}-2)}=\dfrac{\sqrt3(2-\sqrt3)}{3(\sqrt{3}-2)}=-\dfrac{\sqrt{3}}{3} \end{align*}