Запишиверныйответ

Найдизначениевыражения.

\(\cfrac{16^{\log\_{4}\sqrt{3}}\cdot\log\_{3}4+\log\_{3}0,5}{\log\_{3}7-\log\_{3}14}\)

Решение.

\(\cfrac{16^{\log\_{4}\sqrt{3}}\cdot\log\_{3}4+\log\_{3}0,5}{\log\_{3}7-\log\_{3}14}=\cfrac{4^{2\log\_{4}\sqrt{3}}\cdot\log\_{3}4+\log\_{3}0,5}{\log\_{3}\cfrac{7}{14}}=\cfrac{(\sqrt{3})^2\log\_{3}4+\log\_{3}0,5}{\log\_{3}0,5}=\cfrac{\log\_{3}4^3+\log\_{3}0,5}{\log\_{3}0,5}=\cfrac{\log\_{3}(64\cdot0,5)}{\log\_{3}0,5}=\cfrac{\log\_{3}32}{\log\_{3}\cfrac{1}{2}}=\cfrac{\log\_{3}2^5}{\log\_{3}2^{-1}}=\cfrac{5\log\_{3}2}{-1\cdot\log\_{3}2}=\) [ ]