Cho \({{\log }_{2}}\left( {{\log }_{3}}\left( {{\log }_{4}}x \right) \right)={{\log }_{3}}\left( {{\log }_{4}}\left( {{\log }_{2}}y \right) \right)\) \(={{\log }_{4}}\left( {{\log }_{2}}\left( {{\log }_{3}}z \right) \right)=0\). Hãy tính \(S=x+y+z\)
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
Lời giải:
Báo sai\(\begin{array}{*{20}{l}}
\begin{array}{l}
\left\{ {\begin{array}{*{20}{l}}
{{{\log }_2}\left( {{{\log }_3}\left( {{{\log }_4}x} \right)} \right) = 0}\\
{{{\log }_3}\left( {{{\log }_4}\left( {{{\log }_2}y} \right)} \right) = 0}\\
{{{\log }_4}\left( {{{\log }_2}\left( {{{\log }_3}z} \right)} \right) = 0}
\end{array}} \right. \Leftrightarrow \left\{ {\begin{array}{*{20}{l}}
{{{\log }_3}\left( {{{\log }_4}x} \right) = 1}\\
{{{\log }_4}\left( {{{\log }_2}y} \right) = 1}\\
{{{\log }_2}\left( {{{\log }_3}z} \right) = 1}
\end{array}} \right.\\
\Leftrightarrow \left\{ {\begin{array}{*{20}{l}}
{{{\log }_4}x = 3}\\
{{{\log }_2}y = 4}\\
{{{\log }_3}z = 2}
\end{array}} \right. \Leftrightarrow \left\{ {\begin{array}{*{20}{l}}
{x = 64}\\
{y = 16}\\
{z = 9}
\end{array}} \right.
\end{array}\\
{ \Rightarrow x + y + z = 89}
\end{array}\)
Chọn đáp án B
