Question

Упростить выражение
Заранее спасибо :)

Answer 1

Ответ:

0.5

Объяснение:

$\displaystyle\\\frac{log^2_{35}5-2log_{35}5\cdot\\log_{35}7-3log^2_{35}7}{2(log_{35}5-3log_{35}7)} =\\\\\\\frac{(log^2_{35}5-2log_{35}5\cdot\\log_{35}7+log^2_{35}7)-4log^2_{35}7}{2(log_{35}5-3log_{35}7)} =\\\\\\\frac{(log_{35}5-log_{35}7)^2-(2log_{35}7)^2}{2(log_{35}5-3log_{35}7)} =\\\\\\\frac{(log_{35}5-log_{35}7+2log_{35}7)(log_{35}5-log_{35}7-2log_{35}7)}{2(log_{35}5-3log_{35}7)}=\\\\\\\frac{(log_{35}5+log_{35}7)(log_{35}5-3log_{35}7)}{2(log_{35}5-3log_{35}7)}=\\\\\\\frac{log_{35}5+log_{35}7}{2} =$

$\displaystyle\\\frac{log_{35}(5*7)}{2}=\frac{1}{2}$