Question

найдите значение числогого выражения.

Answer 1

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