Question

необходимо вычислить, логарифм

Answer 1

$log_{5^{frac{1}{2} }}frac{25}{sqrt{3}+sqrt{14}} +log_{5^{-1}}(17+2sqrt{42} )^{-1}=log_{5}(frac{25}{sqrt{3}+sqrt{14}})^2 +\ \ +log_{5}(17+2sqrt{42} )= log_{5}frac{25^2}{17+2sqrt{42}} +log_{5}(17+2sqrt{42} )= \ \ =log_525^2-log_{5}(17+2sqrt{42} )+log_{5}(17+2sqrt{42} )=log_5(5^2)^2= \ \ =log_55^4=4 \ \ OTBET: 4$