Question

необходимо вычислить, логарифм

Answer 1

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