Question

Вычислите:
log₂ (9+$sqrt[3]{2 sqrt{5}-3 sqrt{3} } * sqrt[6]{47+12 sqrt{15} } * sqrt[3]{49}$)

Answer 1

$log_{2}(9+sqrt[3]{2sqrt{5}-3sqrt{3}}*sqrt[6]{47+12sqrt{15}}*sqrt[3]{49}})=\\ log_{2}(9+sqrt[3]{(2sqrt{5}-3sqrt{3})*49}*sqrt[6]{47+12sqrt{15}})=\\ log_{2}(9+sqrt[3]{98sqrt{5}-147sqrt{3}}*sqrt[6]{47+12sqrt{15}})=\\ log_{2}(9+sqrt[6]{(98sqrt{5}-147sqrt{3})^2(47+12sqrt{15})}=\\ log_{2}(9+sqrt[6]{(98^2*5-2*98*143sqrt{15}+147^2*3)(47+12sqrt{15})})=\\ log_{2}(9+sqrt[6]{117649})=log_{2}(9+7)=4$