Question

Resolva a equação: log₄ 2x+ log₄ (9-x)=2​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log_4\:2x + log_4\:(9 - x) = 2}$

$\mathsf{log_4\:2x + log_4\:(9 - x) = log_4\:4^2}$

$\mathsf{log_4\:2x(9 - x) = log_4\:16}$

$\mathsf{log_4\:(18x - 2x^2) = log_4\:16}$

$\mathsf{18x - 2x^2 = 16}$

$\mathsf{x^2 - 9x + 8 = 0}$

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

$\mathsf{\Delta = (-9)^2 - 4.1.8}$

$\mathsf{\Delta = 81 - 32}$

$\mathsf{\Delta = 49}$

$\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{9 \pm \sqrt{49}}{2} \rightarrow \begin{cases}\mathsf{x' = \dfrac{9 + 7}{2} = \dfrac{16}{2} = 8}\\\\\mathsf{x'' = \dfrac{9 - 7}{2} = \dfrac{2}{2} = 1}\end{cases}}$

$\boxed{\boxed{\mathsf{S = \{8;1\}}}}$