Question

Вычислите 3 ^log корень 3 ^(5-корень15)+log 1/3 (корень 5 -корень 3)^2

Answer 1

$3^{log_{sqrt3}(5-sqrt{15})+log_{frac{1}{3}}(sqrt5-sqrt3)^2}=3^{log_3(5-sqrt{15})^2-log_3(sqrt5-sqrt3)^2}=\\=3^{log_3 frac{(5-sqrt{15})^2}{(sqrt5-sqrt3)^2} }=( frac{sqrt5cdot (sqrt5-sqrt3)}{sqrt5-sqrt3} )^2=(sqrt5)^2=5$