2logx (27) - 3log27 (x) = 1

Question

Математика

Леонтий

12 мая, 18:17

2logx (27) - 3log27 (x) = 1

+4

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Антония · Answer 1

2 / log27 (x) - 3log 27 (x) = 1

Домножим на log 27 (x) :

2 - 3log² 27 (x) = log 27 (x)

log 27 (x) = t

3t² + t - 2 = 0

D = 1 + 24 = 25

t = (-1-5) / 6 = - 1 t = (-1 + 5) / 6 = 2/3

log 27 (x) = - 1 log 27 (x) = 2/3

x = 1/27 x = 27^ (2/3) = ∛27² = 3² = 9