Question

Решите.................

Answer 1

$1)\ \ 3*(( frac{1}{6} )^{2+log_{ frac{1}{6}}20}- sqrt{2}^{4+log_{ sqrt{2}} frac{1}{9}})=\ \ 3*(( frac{1}{6} )^{log_{ frac{1}{6} } frac{1}{36} +log_{ frac{1}{6}}20}- sqrt{2}^{log_{ sqrt{2} }4+log_{ sqrt{2}} frac{1}{9}}) = \ \ 3*(( frac{1}{6} )^{log_{ frac{1}{6}} frac{20}{36} }- sqrt{2}^{log_{ sqrt{2}} frac{4}{9}}) = \ \ 3*( frac{20}{36} - frac{4}{9}) = 3*( frac{20}{36} - frac{16}{36}) = \ \ = 3*frac{4}{36} = 3*frac{1}{9} = frac{1}{3}$
$2)\\ 25^{log_{5}3 - log_{125}2}-3^{-log_{3}8} = \\ = 25^{2log_{25}3-frac{1}{2}log_{25}2} - frac{1}{3^{log_{3}8}} = \\ = 5^{4log_{25}3-log_{25}2} - frac{1}{3^{3log_{3}2}} = \\ = 5^{log_{25}3^{4}-log_{25}2} - frac{1}{8}} = \\ = 5^{log_{25}frac{3^{4}}{2}} - frac{1}{8}} = \\ = 5^{frac{1}{2}log_{5}frac{3^{4}}{2}} - frac{1}{8}} = \\ = sqrt{frac{3^{4}}{2}} - frac{1}{8} = \\ = frac{9}{sqrt{2}} - frac{1}{8} =$
$= frac{9sqrt{2}}{2} - frac{1}{8} = frac{36sqrt{2}}{8}-frac{1}{8} = frac{36sqrt{2}-1}{8}$