Question

Resolva a equação:

log[(5x-10).(x-2)] = 1 + log8

Por favor

Answer 1

• Use as propriedades logarítmicas.

log[(5x - 10)(x - 2)] = 1 + log 8

log[(5x - 10)(x - 2)] = log 10 + log 8

log[(5x - 10)(x - 2)] = log (10 . 8)

log[(5x - 10)(x - 2)] = log 80

(5x - 10)(x - 2) = 80

5x² - 10x - 10x + 20

5x² - 20x + 20 = 80

x² - 4x + 4 = 16

(x - 2)² = 16

(x - 2)² = 4²

x - 2 = ± 4

x = 2 ± 4

x1 = 2 + 4

x1 = 6

x2 = 2 - 4

x2 = - 2, as duas raízes servem

Resposta: x = 6 ou x = - 2