ĐKXĐ: ...
\(\Leftrightarrow log_3\left(2x-1\right)-log_3\left(x-1\right)^2=3\left(x^2-2x+1\right)-2x+1+1\)
\(\Leftrightarrow log_3\left(2x-1\right)+2x-1=log_3\left(x-1\right)^2+1+3\left(x-1\right)^2\)
\(\Leftrightarrow log_3\left(2x-1\right)+2x-1=log_33\left(x-1\right)^2+3\left(x-1\right)^2\)
Xét hàm \(f\left(t\right)=log_3t+t\) với \(t>0\)
\(f'\left(t\right)=\frac{1}{t.ln3}+1>0\Rightarrow f\left(t\right)\) đồng biến
\(\Rightarrow f\left(2x-1\right)=f\left(3\left(x-1\right)^2\right)\Leftrightarrow2x-1=3\left(x-1\right)^2\)
\(\Leftrightarrow3x^2-8x+4=0\)
\(\Leftrightarrow...\)
