Question

Determine a alternativa correta referente ao conjunto solução da equação logarítmica a seguir:
A.
S = {7}

B.
S = {-7}

C.
S = {-11 e 7}

D.
S = {-11}

E.
S = {-7 e 11}

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log_3\:(x + 2) + log_3\:(3x + 6) = 5 }$

$\mathsf{log_3\:(x + 2).(3x + 6) = log_3\:243 }$

$\mathsf{3x^2 + 6x + 6x + 12 = 243}$

$\mathsf{3x^2 + 12x - 231 = 0}$

$\mathsf{x^2 + 4x - 77 = 0}$

$\mathsf{\Delta = b^2 - 4.a.c}$

$\mathsf{\Delta = (4)^2 - 4.1.(-77)}$

$\mathsf{\Delta = 16 + 308}$

$\mathsf{\Delta = 324}$

$\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{-4 \pm \sqrt{324}}{2} \rightarrow \begin{cases}\mathsf{x' = \dfrac{-4 + 18}{2} = \dfrac{14}{2} = 7}\\\\\mathsf{x'' = \dfrac{-4 - 18}{2} = -\dfrac{22}{2} = -11}\end{cases}}$

$\boxed{\boxed{\mathsf{S = \{7\}}}}\leftarrow\textsf{letra A}$