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6-log-16-x-4-3-2log-16-x-2-lt-2-

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Question Number 84674 by jagoll last updated on 15/Mar/20
((6−log_(16) (x^4 ))/(3+2log_(16) (x^2 ))) < 2
6−log16(x4)3+2log16(x2)<2
Commented by jagoll last updated on 15/Mar/20
(i) x ≠ 0 ⇒ ((6−2log_(16) (x^2 ))/(3+2log_(16) (x^2 ))) < 2 ⇒ ((3−log_(16) (x^2 ))/(3+2log_(16) (x^2 ))) < 1 let t = log_(16) (x^2 ) ((3−t)/(3+2t))−((3+2t)/(3+2t)) < 0 ((−3t)/(3+2t)) <0 ⇒ t<−(3/2) ∨t > 0 log_(16) (x^2 ) < log_(16) (16)^(−(3/2)) ∨ log_(16) (x^2 ) > log_(16) (16)^0 x^2 < (1/(64)) ∨ x^2 > 1⇒ x<−1 ∨ −(1/8)<x<(1/8) ∨ x > 1
(i)x≠0⇒6−2log16(x2)3+2log16(x2)<2⇒3−log16(x2)3+2log16(x2)<1lett=log16(x2)3−t3+2t−3+2t3+2t<0−3t3+2t<0⇒t<−32∨t>0log16(x2)<log16(16)−32∨log16(x2)>log16(16)0x2<164∨x2>1⇒x<−1∨−18<x<18∨x>1

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