Đáp án:
$S = \left\{\dfrac{5}{2};6\right\}$
Giải thích các bước giải:
$\begin{array}{l}(x-2)^{\log_24(x-2)} = 2^2(x-2)^3\qquad (*)\\ ĐK: x > 2\\ (*) \Leftrightarrow \log_2[(x-2)^{\log_24(x-2)}] = \log_2[2^2(x-2)^3]\\ \Leftrightarrow \log_24(x-2).\log_2(x-2) = \log_24(x-2)^3\\ \Leftrightarrow [\log_24 + \log_2(x-2)].\log_2(x-2) = \log_24 + \log_2(x-2)^3\\ \Leftrightarrow 2\log_2(x-2) + \log_2^2(x-2) = 2 + 3\log_2(x-2)\\ \Leftrightarrow \log_2^2(x-2) - \log_2(x-2) - 2 = 0\\ \Leftrightarrow \left[\begin{array}{l}\log_2(x-2) = -1\\\log_2(x-2) = 2\end{array}\right.\\ \Leftrightarrow \left[\begin{array}{l}x - 2 = 2^{-1}\\x - 2 = 2^2\end{array}\right.\\ \Leftrightarrow \left[\begin{array}{l}x = \dfrac{5}{2}\\x =6\end{array}\right.\quad (nhận)\\ Vậy \,\,S = \left\{\dfrac{5}{2};6\right\} \end{array}$