Resposta:

[tex]\textsf{Leia abaixo}[/tex]

Explicação passo a passo:

[tex]\sf log\:3\:.\:(x - 1)^2 = 2[/tex]

[tex]\sf log\:3\:.\:(x^2 - 2x + 1) = log 10^2[/tex]

[tex]\sf log\:(3x^2 - 6x + 3) = log\:100[/tex]

[tex]\sf 3x^2 - 6x + 3 = 100[/tex]

[tex]\sf 3x^2 - 6x - 97 = 0[/tex]

[tex]\sf a = 3 \Leftrightarrow b = -6 \Leftrightarrow c = -97[/tex]

[tex]\sf \Delta = b^2 - 4.a.c[/tex]

[tex]\sf \Delta = (-6)^2 - 4.3.(-97)[/tex]

[tex]\sf \Delta = 36 + 1.164[/tex]

[tex]\sf \Delta = 1.200[/tex]

[tex]\sf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{6 \pm \sqrt{1.200}}{6} \rightarrow \begin{cases}\sf{x' = \dfrac{6 + 20\sqrt{3}}{6} = \dfrac{3 + 10\sqrt{3}}{3}}\\\\\sf{x'' = \dfrac{6 - 20\sqrt{3}}{6} = \dfrac{3 - 10\sqrt{3}}{3}}\end{cases}}[/tex]

[tex]\boxed{\boxed{\sf S = \left\{\dfrac{3 + 10\sqrt{3}}{3}\:,\dfrac{3 - 10\sqrt{3}}{3}\right\}}}[/tex]