Question

Resolva em R a equação Log ($\frac{x}{5}$X-2) + log (X-3) = log $\frac{20}{5}$

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log_5\:(x - 2) + log_5\:(x - 3) = log_5\:20}$

$\mathsf{log_5\:(x - 2).(x - 3) = log_5\:20}$

$\mathsf{(x - 2).(x - 3) = 20}$

$\mathsf{x^2 - 3x - 2x + 6 = 20}$

$\mathsf{x^2 - 5x - 14 = 0}$

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

$\mathsf{\Delta = (-5)^2 - 4.1.(-14)}$

$\mathsf{\Delta = 25 + 56}$

$\mathsf{\Delta = 81}$

$\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{5 \pm \sqrt{81}}{2} \rightarrow \begin{cases}\mathsf{x' = \dfrac{5 + 9}{2} = \dfrac{14}{2} = 7}\\\\\mathsf{x'' = \dfrac{5 - 9}{2} = -\dfrac{4}{2} = -2}\end{cases}}$

$\boxed{\boxed{\mathsf{S = \{7\}}}}$