Монгол Бодлогын Сан

Заавар:$2\log_43=\log_{4^{\frac12}}3=\log_23$, $8^{\frac13}=2$ ашигла.

Бодолт:\begin{align*} \text{Илэрх.}&=\left(3^{1+\frac{1}{2\log_43}}+8^{\frac{1}{3\log_92}}+1\right)^{0.5}\\ &=\left(3^{1+\frac{1}{\log_23}}+(8^{\frac{1}{3}})^{\frac{1}{\log_92}}+1\right)^{0.5}\\ &=\left(3\cdot 3^{\frac{1}{\log_23}}+2^{\frac{1}{\log_92}}+1\right)^{0.5} & & \color{WildStrawberry}{\leftarrow\dfrac{1}{\log_ab}=\log_ba}\\ &=\left(3\cdot 3^{\log_32}+2^{\log_29}+1\right)^{0.5} & & \color{WildStrawberry}{\leftarrow a^{\log_ab}=b}\\ &=(3\cdot 2+9+1)^{0.5}=16^{0.5}=4 \end{align*}