Question

Найдите значение выражения (основания у логарифмов 3)
0,5*log(5-2*6^(1/2))+log(3^(1/2)+2^(1/2))

Answer 1

$0.5log_{3}(5-2*6^{frac{1}{2}})+log_{3}(3^{frac{1}{2}}+2^{frac{1}{2}})= \ 0.5log_{3}(5-2 sqrt{6})+0.5log_{3}((sqrt{3}+sqrt{2})^{2})= \ 0.5log_{3}(5-2 sqrt{6})+0.5log_{3}(3+2 sqrt{2*3} +2)= \ 0.5log_{3}(5-2 sqrt{6})+0.5log_{3}(5+2 sqrt{6})= \ 0.5log_{3}((5-2 sqrt{6})*(5+2 sqrt{6}))= \ 0.5log_{3}(5^{2}-(2sqrt{6})^{2})= \ 0.5log_{3}1=0$