Question

Determine o valor de x: log2 x + log2 (x − 2) = 3​

Answer 1

Resposta:

x = 4

Explicação passo a passo:

$log__2x+log_2(x-2)=3$

C.E: x > 0 e x - 2 > 0 ⇒ x > 2

$log_2x(x-2)=2$

x(x - 2) = 2³

x² - 2x = 8

x² - 2x - 8 = 0

Δ = -(-2)² - 4.1(-8)]

Δ = 4 + 32

Δ = 36

$\Delta=\frac{-(-2)\pm\sqrt{36} }{2.1} \\\\x=\frac{2\pm6}{2}\\\\x=\frac{8}{2} =4\\\\ou\\\\x=\frac{-4}{2}=-2 ~~(n\tilde a o~~serve)$