ĐKXĐ: \(x>0\)
\(log_2^2x-m.log_2x-log_2x+m=0\)
\(\Leftrightarrow log_2x\left(log_2x-m\right)-\left(log_2x-m\right)=0\)
\(\Leftrightarrow\left(log_2x-1\right)\left(log_2x-m\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x_1=2\\x_2=2^m\end{matrix}\right.\)
TH1: \(x_1=x_2^2\Leftrightarrow2=\left(2^m\right)^2=2^{2m}\Rightarrow2m=1\Rightarrow m=\dfrac{1}{2}\)
TH2: \(x_2=x_1^2\Rightarrow2^m=2^2\Rightarrow m=2\)
\(\Rightarrow2+\dfrac{1}{2}=\dfrac{5}{2}\)
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