smc

Let ${\log }_{10}x=a$, so $10^a=x$. Note that $10^0=1$ and that $10^a$ increases as $a$ increases. Since $a<0$, $10^a<1$. However, for all $a$, $10^a>0$, so $0<x<1$. The answer is $\boxed{0<x<1}$.