Question

Determine o conjunto solução da equação logaritma log×(x+20)=2

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log_x\:(x + 20) = 2}$

$\mathsf{x^2 = x + 20}$

$\mathsf{x^2 - x - 20 = 0}$

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

$\mathsf{\Delta = (-1)^2 - 4.1.(-20)}$

$\mathsf{\Delta = 1 + 80}$

$\mathsf{\Delta = 81}$

$\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{1 \pm \sqrt{81}}{2} \rightarrow \begin{cases}\mathsf{x' = \dfrac{1 + 9}{2} = \dfrac{10}{2} = 5}\\\\\mathsf{x'' = \dfrac{1 - 8}{2} = -\dfrac{8}{2} = -4}\end{cases}}$

$\boxed{\boxed{\mathsf{S = \{5\}}}}$