ĐK: $x>0$, khi đó $\lg x^2=2\lg x$Pt $\Leftrightarrow 4.4^{\lg x}-6^{\lg x}-2.3^{2\lg x+2}=0$
$\Leftrightarrow 4.4^{\lg x}-6^{\lg x}-18.9^{\lg x}=0$
Chia cả 2 vế cho $4^{\lg x},$ta được:
$4-(\frac{3}{2})^{\lg x}-18.(\frac{9}{4})^{\lg x}=0 (*)$
Đặt $t=(\frac{3}{2})^{\lg x} (t>0)$
Pt$(*)\Leftrightarrow 18t^2+t-4=0\Leftrightarrow t=\frac{-1}{2}(loại)\vee t=\frac{4}{9}$
$\Rightarrow (\frac{3}{2})^{\lg x}=\frac{4}{9}=(\frac{3}{2})^{-2}\Leftrightarrow \lg x=-2\Leftrightarrow x=10^{-2}$