Question

Найдите значение выражения ​

Answer 1

$\frac{3log_{9}^{2}14-4log_{9}42*log_{9} 14+log_{9}^{2}42}{3log_{9}14-log_{9} 42}=\frac{3(log_{9}14-\frac{1}{3} log_{9} 42)(log_{9}14-log_{9}42)}{3log_{9}14-log_{9}42)} =\\\\\frac{(3log_{9}14-log_{9}42)(log_{9}14-log_{9}42)}{log_{9}14-log_{9} 42} =log_{9}14-log_{9}42=log_{9}\frac{14}{42} =\\\\=log_{9}\frac{2}{6}=log_{9}\frac{1}{3}=log_{9}3^{-1}=-log_{9}3=\boxed{-0,5}$