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),∞) ★