[latex]log_4{x}+log_2{x}=log_{0.5}\sqrt{8}[/latex]

[latex]log_4{x}+log_2{x}=log_{0.5}\sqrt{8}[/latex] ОДЗ: [latex]x\ \textgreater \ 0[/latex] [latex]log_{2^2}{x}+log_2{x}=log_{2^{-1}}\sqrt{8}[/latex] [latex] \frac{1}{2} log_{2}{x}+log_2{x}=-log_{2}\sqrt{8}[/latex] [latex]1 \frac{1}{2} log_{2}{x}=-log_{2}\sqrt{8}[/latex] [latex]1 \frac{1}{2} log_{2}{x}=-log_{2}2^{ \frac{3}{2}} [/latex] [latex]\frac{3}{2} log_{2}{x}=- \frac{3}{2} log_{2}2[/latex] [latex]\frac{3}{2} log_{2}{x}=- \frac{3}{2} [/latex] [latex]log_{2}{x}=-1[/latex] [latex]x=2^{-1}[/latex] [latex]x= \frac{1}{2} [/latex] Ответ: [latex] \frac{1}{2} [/latex]