Question Number 101553 by bobhans last updated on 03/Jul/20

solve the inequality  ( ^3 log x+2)^(5x+1)  ≥ ( ^3 log x +2)^(3−3x)

Answered by bramlex last updated on 03/Jul/20

→(log _3  x+2−1)(5x+1−3+3x)≥0  (log _3 x +1)(8x−2)≥0  case(1) log _3 x+1≥0 ∧8x−2≥0                  x ≥(1/3) ∧ x≥(1/4) ⇔x≥(1/3)  case(2) log _3 x +1≤0 ∧ 8x−2≤0   x ≤(1/3) ∧x≤(1/4) ∧x > 0⇒0< x ≤(1/4)  we get solution is   x∈ (0, (1/4)] ∪ [ (1/3),∞) ★