Question

Помогите. 1) X^(lg^2 x-3lgx+1)>1000. 2) 5^logx49-7^logx5-2>=0

Answer 1

X^(lg^2 x-3lgx+1)>1000
lgX^(lg^2 x-3lgx+1)>lg1000
(lg^2 x-3lgx+1)lgx>3
lg^3 x-3lg^2x+lgx-3>0
lg^2x(lgx-3)+(lgx-3)>0
(lgx-3)(lg^2x+1)>0
lg^2x+1>0  всегда
lgx-3>0
lgx>3
x>1000
2) 5^logx49-7^logx5-2>=0
49^logx5-7^logx5-2>=0
7^2logx5-7^logx5-2>=0
7^logx5=t, t>0
t^2-t-2>=0
(t+1)(t-2)>=0, t>0
t>=2
 7^logx5>=2
logx5>=log7(2)
x^log7(2)>=5
x>=5^log2(7)