Ответ:
1/10;1000
Объяснение:
![x^{\log_{10} x} = 1000 *x^{2} x^{\log_{10} x} = 1000 *x^{2}](https://tex.z-dn.net/?f=x%5E%7B%5Clog_%7B10%7D%20x%7D%20%3D%201000%20%2Ax%5E%7B2%7D)
log(10, x^(log(10, x))=log(10, 1000x^2)
log(10, x)*log(10, x)=log(10, 1000)+log(10, x^2)
log^2(10, x)=3+2log(10, x)
log^2(10, x)-2log(10, x) -3 =0
y=log(10, x)
y^2-2y-3=0
(y+1)(y-3)=0
y+1=0 or y-3=0
y=-1 or y=3
log(10, x)=-1 or log(10, x)=3
1.lnx=-ln10
lnx=ln(1/10)
x=1/10
2.lnx=3ln10
lnx=ln1000
x=1000