Вычислите:log₂ (9+[tex] \sqrt[3]{2 \sqrt{5}-3 \sqrt{3} } * \sqrt[6]{47+12 \sqrt{15} } * \sqrt[3]{49} [/tex]). Created by nikolson93. algebra-ru

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nikolson93 @nikolson93

August 2022 1 20 Report

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

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

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