Question

log(2)(x+4)+2log(2)(1/2-x)=0

Answer 1

㏒₂ (x+4) + 2㏒₂(1/(2 - x)) = 0
Одз
x+ 4 > 0, x  > -4
1/(2 - x) > 0, x < 2
㏒₂ (x+4) = -2㏒₂($frac{1}{x-2}$)
㏒₂ (x+4)  = ㏒₂ ($frac{1}{x-2}$)⁻²
x+4 = (x-2)²
x + 4 = x² - 4x + 4
x(x-3) = 0
x₁ = 3(не удв-т ОДЗ)
x₂ = 0