Đáp án:
\(x = \frac{{1 + \sqrt 5 }}{2}\)
Giải thích các bước giải:
\(\begin{array}{l}
\,\,\,\,\,{\log _2}x - {\log _{0,5}}\left( {x - 1} \right) = 0\,\,\left( {x > 1} \right)\\
\Leftrightarrow {\log _2}x - {\log _{{2^{ - 1}}}}\left( {x - 1} \right) = 0\\
\Leftrightarrow {\log _2}x + {\log _2}\left( {x - 1} \right) = 0\\
\Leftrightarrow {\log _2}\left[ {x\left( {x - 1} \right)} \right] = 0\\
\Leftrightarrow x\left( {x - 1} \right) = 1\\
\Leftrightarrow {x^2} - x - 1 = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x = \frac{{1 + \sqrt 5 }}{2}\,\,\left( {tm} \right)\\
x = \frac{{1 - \sqrt 5 }}{2}\,\,\left( {ktm} \right)
\end{array} \right.
\end{array}\)
