Question Number 100409 by Algoritm last updated on 26/Jun/20

Commented bybramlex last updated on 26/Jun/20

(((3/2)×4^x )/(4^x −9^x )) > 3+ ((4/9))^x   ((3.((4/9))^x )/(2{((4/9))^x −1})) > 3+((4/9))^x   let ((4/9))^x = z > 0 _(1)  ((3z)/(2(z−1))) > 3+z ⇒((3z−(3+z)(z−1))/(2(z−1))) > 0  ((3z−(z^2 +2z−3))/(z−1)) > 0  ((z^2 −z−3)/(z−1)) < 0 ⇒(((z−(1/2))^2 −((13)/4))/(z−1)) < 0  (((z−(1/2)−((√(13))/2))(z−(1/2)+((√(13))/2)))/(z−1)) < 0  z < ((1−(√(13)))/2) or 1< z < ((1+(√(13)))/2)  _(2)  solution for z : (1)∩(2)  1 < z < ((1+(√(13)))/2) ⇒ 1< ((4/9))^x <((1+(√(13)))/2)  log _(((4/9))) (((1+(√(13)))/2)) < x < 0   −1.0285 < x < 0

Commented byAlgoritm last updated on 26/Jun/20