Question

Os valores de x que satisfazem log x + log (x – 8) = log 20 são: *
10
-2
10 e 2
10 e -2​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log\:x + log\:(x - 8) = log\:20}$

$\mathsf{log\:x(x - 8) = log\:20}$

$\mathsf{x(x - 8) = 20}$

$\mathsf{x^2 - 8x - 20 = 0}$

$\mathsf{x^2 - 8x - 20 + 36 = 0 + 36}$

$\mathsf{x^2 - 8x + 16 = 36}$

$\mathsf{(x - 4)^2 = 36}$

$\mathsf{x - 4 = \pm\:\sqrt{36}}$

$\mathsf{x - 4 = \pm\:6}$

$\mathsf{x' = 6 + 4 = 10}$

$\mathsf{x'' = -6 + 4 = -2}$

$\boxed{\boxed{\mathsf{S = \{10;-2\}}}}$