Resposta:
[tex]\textsf{Leia abaixo}[/tex]
Explicação passo a passo:
[tex]\mathsf{log^2\:x - 7\:log\:x + 10 = 0}[/tex]
[tex]\mathsf{y = log\:x}[/tex]
[tex]\mathsf{y^2 - 7y + 10 = 0}[/tex]
[tex]\mathsf{\Delta = b^2 - 4.a.c}[/tex]
[tex]\mathsf{\Delta = (7)^2 - 4.1.10}[/tex]
[tex]\mathsf{\Delta = 49 - 40}[/tex]
[tex]\mathsf{\Delta = 9}[/tex]
[tex]\mathsf{y = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{7 \pm \sqrt{9}}{2} \rightarrow \begin{cases}\mathsf{y' = \dfrac{7 + 3}{2} = \dfrac{10}{2} = 5}\\\\\mathsf{y'' = \dfrac{7 - 3}{2} = \dfrac{4}{2} = 2}\end{cases}}[/tex]
[tex]\mathsf{log\:x = 5}[/tex]
[tex]\mathsf{x = 10^5 = 100.000}[/tex]
[tex]\mathsf{log\:x = 2}[/tex]
[tex]\mathsf{x = 10^2 = 100}[/tex]
[tex]\boxed{\boxed{\mathsf{S = \{100;100.000\}}}}[/tex]
