Question

log5(5x-27) / log5(x-5) ≥ 1

Answer 1

ОДЗ x-5>0  x>5  log5(x-5)≠0  x-5≠1  x≠6

5х-27>0  5x>27  x>5,4

log5((5x-27)/(x-5))/log5(x-5)>=0

log5(5x-27)/(x-5)>=log5(1)

log5(x-5)>=log5(1)

(5x-27)/(x-5)>=1   (5x-27-x+5)/(x-5)>=0  (4x-22)/(x-5)>=0

(x-5,5)/(x-5)>=0  x>5,5

x-5>=1   x>=6

log5(5x-27)/(x-5)<=log5(1)

log5(x-5)<=log5(1)  x-5<=1   x<=6    

(5x-27)/(x-5)<=1   (4x-22)/(x-5)<=0   [5;5,5]

[5;6]  

с учетом ОДЗ  (5,4;5,5] U (6;∞)