Question

qual o log 2(x-2) +log2 x=3 ?

Answer 1

㏒₂ (x-2) + ㏒₂ x = 3


Aplicando as propriedades dos logaritmos:

㏒₂ x(x-2) = 3
x(x-2) = 2³
x² - 2x = 8
x² - 2x -8 = 0

Δ = (-2)² - 4(1)(-8)
Δ = 4 + 32
Δ = 36

$x = \frac{2~\pm~6}{2} \\ \\ x'= \frac{2~+~6}{2} =4 \\ \\ x''= \frac{2~-~6}{2}=-2$


S = {-2; 4}