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

Question

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

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

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