Question

(1/25)^x-26(1/5)^x+25<=0

Answer 1

сделаем замену y=(1/5)^x
y^2-26y+25<=0
решим уравнение y^2-26y+25=0
D=26^2-4*25=576, √D=24
y1=1 и y2=25
ответ для нераенства с y
1<=y<=25
1<=(1/5)^x<=25
ln1<=ln(1/5)^x<=ln25
ln1<=x*ln(1/5)<=2*ln5
ln1<=x*ln5^-1<=2*ln5
ln1<=-x*ln5<=2*ln5
-ln1/ln5>=x>=-2*ln5/ln5
-log₅1>=x>=-2
-2<=x<=-log₅1