Respuesta :

mhanifa

Answer:

  • [ln (4 - x) - ln (x + 1/2)] × [ln (4 - x) + 2 ln (x + 1/2)]  = 0

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Given equation:

  • ln² (4 - x) + ln (4 - x) ln (x + 1/2) - 2 ln² (x + 1/2) = 0

Substitute:

  • ln (4 - x) = p, ln (x + 1/2) = q

Then we have:

  • p² + pq - 2q² =
  • p² - q² + pq - q² =
  • (p + q)(p - q) + q(p - q) =
  • (p - q)(p + q + q) = 0
  • (p - q)(p + 2q) = 0

Substitute back:

  • ln² (4 - x) + ln (4 - x) ln (x + 1/2) - 2 ln² (x + 1/2) = 0
  • [ln (4 - x) - ln (x + 1/2)] × [ln (4 - x) + 2 ln (x + 1/2)]  = 0

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