6) log₃² x + 3 log₃ x + 9 = 37/(log₃ x/27) ;

log₃² x + 3 log₃ x + 9 = 37/(log₃ x/27)

log₃² x + 3 log₃ x + 9 = 37/(log₃ x - log₃ 27)

log₃² x + 3 log₃ x + 9 = 37/(log₃ x - 3)

Пусть t = log₃ x, тогда:

t² + 3t + 9 = 37/(t - 3)

(t² + 3t + 9)(t - 3) = 37

t³ - 3t² + 3t² - 9t + 9t - 27 = 37

t³ = 64

t = 4

log₃ x = 4

x = 3⁴

x = 81

Ответ: 81