Question

реши неравенство.помогите пожалуйста решить.log5(2x_1)>3.log3(4x-3)<log3(2x+1).log0,3(3x+5)>log0,3(5x-2).

Answer 1

1)
$log_5(2x-1) textgreater 3$
ОДЗ: $2x-1 textgreater 0;x textgreater 0.5$
$log_5(2x-1) textgreater log_5 125$
$2x-1 textgreater 125$
$x textgreater 63$

2) 
$log_3(4x-3) textless log_3(2x+1)$
ОДЗ:
$left { {{4x-3 textgreater 0} atop {2x+1 textgreater 0}} right. ; left { {{x textgreater 0.75} atop {x textgreater -0.5}} right. ;x textgreater 0.75$
$4x-3 textless 2x+1$
$2x textless 4$
$x textless 2$
С учетом ОДЗ: $(0,75;2)$

3)
$log_{0.3}(3x+5) textgreater log_{0.3}(5x-2}$
ОДЗ:
$left { {{3x+5 textgreater 0} atop {5x-2 textgreater 0}} right. ; left { {{x textgreater -5/3} atop {x textgreater 0.4}} right. ; x textgreater 0.4$
$3x+5 textless 5x-2$
$2x textgreater 7$
$x textgreater 3.5$