Question

Помогите решить пример

Answer 1

$log_{2}\frac{1}{2}+log_{4} 2+log_{8}4=log_{2}\frac{1}{2}+log_{4^{\frac{1}{2}}}2^{\frac{1}{2}}}+log_{8^{\frac{1}{3}}}4^{\frac{1}{3}}= log_{2}\frac{1}{2}+log_{2}2^{\frac{1}{2}} +log_{2}4^{\frac{1}{3}}=\\\\=log_{2}2^{-1} +log_{2}2^{\frac{1}{2}}+log_{2}2^{\frac{2}{3}} =log_{2}(2^{-1}*2^{\frac{1}{2}}*2^{\frac{1}{3}})=log_{2}2^{-1+\frac{1}{2}+\frac{1}{3}} =\\\\=log_{2} 2^{\frac{5}{6}}=\frac{5}{6}log_{2}2=\frac{5}{6}$