Найдите значение числогого выражения.

Воспользуемся свойством логарифма
$log_{0.4}(0.2*\sqrt[3]{50})+log_{0.6}(\frac{\sqrt{15}}{5})+log_{0.32}(\frac{2*\sqrt{2}}{5}) =\\\\ 1) log_{0.4}(0.2)+log_{0.4}\sqrt[3]{50} = -log_{0.4}5+\frac{log_{0.4}50}{3} =\\ - log_{0.4}5+\frac{2log_{0.4}5+log_{0.4}2}{3} =\\ \frac{log_{0.4}2-log_{0.4}5}{3}=\frac{log_{0.4}0.4}{3} = \frac{1}{3}\\ \\ 2)\\ log_{0.6}\sqrt{15}-log_{0.6}5=\frac{log_{0.6}15}{2}-log_{0.6}5=\\ \frac{log_{0.6}3 -log_{0.6}5}{2} = \frac{1}{2}\\ 3)\\ log_{0.32}2\sqrt{2}-log_{0.32}5 = \frac{log_{0.32}8-log_{0.32}25}{2} \\$
$=\frac{1}{2}\\ \frac{1}{3}+2*\frac{1}{2}=\frac{4}{3}$