Монгол Бодлогын Сан

Заавар:

Бодолт: \begin{align*} \text{Илэрх.}&=\log^2_{\sqrt[5]5}\sqrt5-\log_{\sqrt[3]5}5\sqrt5+\log_{\sqrt3+1}(4+2\sqrt3)\\ &=\big(\log_{5^{\frac15}}5^{\frac12}\big)^2-\log_{5^{\frac13}}5^{\frac32}+\log_{\sqrt3+1}(\sqrt3+1)^2\\ &=\left(\dfrac{\frac12}{\frac15}\log_55\right)^2-\dfrac{\frac32}{\frac13}\log_55+2\\ &=\dfrac{25}{4}-\dfrac{9}{2}+2=\dfrac{25-18+8}{4}=\dfrac{15}{4}=3.75 \end{align*}