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3-x-2-x-4-7-x-2-find-solution-

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Question Number 83285 by jagoll last updated on 29/Feb/20
3^((x+2)(x−4)) ≤ 7^(x+2) find solution
3(x+2)(x−4)⩽7x+2findsolution
Commented by jagoll last updated on 29/Feb/20
7^(log_7 (3^((x+2)(x−4)) ) ) ≤ 7^(x+2) ⇒ (x+2)(x−4)log_7 (3) ≤ x+2 ⇒ (x+2) [ (x−4)log_7 (3)−1] ≤ 0 −2 ≤ x ≤ 4+ log_3 (7)
7log7(3(x+2)(x−4))⩽7x+2⇒(x+2)(x−4)log7(3)⩽x+2⇒(x+2)[(x−4)log7(3)−1]⩽0−2⩽x⩽4+log3(7)
Answered by MJS last updated on 01/Mar/20
(x+2)(x−4)ln 3 ≤(x+2)ln 7 (1) x+2<0 ⇔ x<−2 (x−4)ln 3 ≥ln 7 x≥((ln 7)/(ln 3))+4 ⇒ no solution (2) x+2≥0 ⇔ x≥−2 for x=−2: 3^((x+2)(x−4)) =7^(x+2) for x>−2: (x−4)ln 3 ≤ln 7 x≤((ln 7)/(ln 3))+4 ⇒ −2≤x≤((ln 7)/(ln 3))+4
(x+2)(x−4)ln3⩽(x+2)ln7(1)x+2<0⇔x<−2(x−4)ln3⩾ln7x⩾ln7ln3+4⇒nosolution(2)x+2⩾0⇔x⩾−2forx=−2:3(x+2)(x−4)=7x+2forx>−2:(x−4)ln3⩽ln7x⩽ln7ln3+4⇒−2⩽x⩽ln7ln3+4

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