Монгол Бодлогын Сан

Заавар: $\log_{a^m}b^n=\dfrac{n}{m}\log_ab$ томьёог ашиглаарай.

Бодолт: \begin{align*} \text{Илэрх.}&=2^{6\log_{2\sqrt2}(5-\sqrt{10})+8\log_{1/4}(\sqrt5-\sqrt2)}\\ &=2^{6\log_{2^{1.5}}(5-\sqrt{10})+8\log_{2^{-2}}(\sqrt5-\sqrt2)}\\ &=2^{\frac{6}{1.5}\log_2(5-\sqrt{10})+\frac{8}{-2}\log_{2}(\sqrt{5}-\sqrt{2})}\\ &=2^{4\log_2(5-\sqrt{10})-4\log_2(\sqrt5-\sqrt2)}\\ &=2^{4\log_2\frac{5-\sqrt{10}}{\sqrt5-\sqrt2}}=2^{4\log_2\frac{\sqrt{5}(\sqrt{5}-\sqrt{2})}{\sqrt5-\sqrt2}}\\ &=2^{4\log_2\sqrt{5}}=2^{\log_2(\sqrt{5})^4}\\ &=2^{\log_225}=25 \end{align*}