Question

помогите решить логарифмы под номерами 17 и 18 пожалуйста )

Answer 1

17)
$log_{0.2} (4x-1) textless log_{0.2} (x+1)$
ОДЗ:
$left { {{4x-1 textgreater 0} atop {x+1 textgreater 0}} right. ; left { {{4x textgreater 1} atop {x textgreater -1}} right. ;left { {{x textgreater 0.25} atop {x textgreater -1}} right. ; x textgreater 0.25$
$4x-1 textgreater x+1$
$3x textgreater 2$
$x textgreater frac{2}{3}$
Ответ: (2/3;+∞)

18)
$log_{0.5}(log_6 (x^2-3)) textgreater 0$
ОДЗ:
$left { {{log_6 (x^2-3) textgreater 0} atop {(x^2-3) textgreater 0}} right. ; left { {{x^2-3 textgreater 1} atop {x^2-3 textgreater 0}} right. ;left { {{x^2 textgreater 4} atop {x^2 textgreater 3}} right. ; left { {{x textless -2} atop {x textgreater 2}} right.$

$log_6 (x^2-3) textless 1$
$log_6 (x^2-3) textless log_6 6$
$x^2-3 textless 6$
$x^2 textless 9$
$-3 textless x textless 3$
C учетом ОДЗ: (-3;-2)∪(2;3)