[tex]\it 2lg^3x+3lg^2x-2lgx=0\\ \\ Not\breve{a}m\ lgx=t,\ iar\ ecua\c{\it t}ia\ devine:\ \ 2t^3+3t^2-2t=0\Rightarrow \\ \\ \Rightarrow t(2t^2+3t-2)=0 \Rightarrow \begin{cases}\it t=0 \Rightarrow lgx=0 \Rightarrow x=10^0=1\\ \\ \it 2t^2+3t-2=0 \Rightarrow t_1=-2,\ \ t_2=\dfrac{1}{2}\end{cases}[/tex]
[tex]\it t=-2 \Rightarrow lgx=-2 \Rightarrow x=10^{-2}=\dfrac{1}{100}\\ \\ t=\dfrac{1}{2}\Rightarrow lgx=\dfrac{1}{2} \Rightarrow x=10^{\frac{1}{2}} =\sqrt{10}[/tex]
Mulțimea soluțiilor ecuației date este:
[tex]\it\ \ S = \left\{\dfrac{1}{100},\ 1,\ \ \sqrt{10}\right\}[/tex]
