Log(3)x/log(3)x/27 ≥ 4/log(3)x + 8/(log^2(3) x - log(3) x^3)
ОДЗ x>0
log x ≠ 0 x≠1
log x/27 ≠ 0 x≠27
log^2(3)x - log(3)x^3≠ 0 x≠1 x≠3³=27
x∈(0 1) U (1 27) U (27 ∞)
log(3) x/27 = log(3)x - log(3) 27 = log(3)x - 3
log^2(3)x - log(3)x^3 = log^2(3) x - 3 log(3) x = log(3)x (log(3) x - 3)
log(3)x=t
t/(t-3) ≥ 4/t + 8/t(t-3)
(t² - 4(t-3) - 8) /t(t-3) ≥ 0
(t² - 4t + 12 -8)/t(t-3) ≥ 0
(t-2)²/t(t-3) ≥ 0
++++++ 0 ------- {2} -------3 ++++++++
t∈(-∞ 0) U {2} U (3 +∞)
log(3) x< 0
x<1<br>log(3) x = 2
x=9
log(3)x>3
x>27
пересекаем с ОДЗ
x = (0 1) U {9} U (27 +∞)