Ensino Médio ⇒ Logaritmo - (Iezzi) 272 Tópico resolvido

[Oziel]

[tex3]x^{2}[/tex3]+x [tex3]log^{5} - log^{2}[/tex3]=0

Resposta

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S={[tex3]log^{2}, -1[/tex3]}

[LucasPinafiMOD]

[tex3]x^2 + x \log 5 - \log 2 = 0 \\ x = \frac{-\log 5 \pm \sqrt{(\log 5)^2 +4 \log 2}}{2} = \frac{-\log 5 \pm \sqrt{(1- \log 2)^2 + 4 \log 2}}{2} = \frac{-\log 5 \pm \sqrt{1+ 2 \log 2 + \log^2 2 }}{2} = \frac{- \log 5 \pm \sqrt{(1+\log 2)^2}}{2} \\ x = \frac{-\log 5 \pm (\log 2 +1)}{2} = \frac{-(1- \log 2) \pm \log 2 +1}{2} \\ x_1 = \frac{2 \log 2}{2} = \log 2 \\ x_2 = \frac{-2}{2} = -1[/tex3]