7. The set 
$\left\{x \left\lvert\,-1 \leqslant \log _{\frac{1}{x}} 10<-\frac{1}{2}\right., x \in \mathbf{N}\right\}$ has $\qquad$ proper subsets.
$$
-1 \leqslant \log _{\frac{1}{x}} 10<-\frac{1}{2} \Rightarrow-2<\lg \frac{1}{x} \leqslant-1 \Rightarrow 1 \leqslant \lg x<2 \Rightarrow 10 \leqslant x \leqslant 99 .
$$

Thus, the set contains 90 elements, so the number of its proper subsets is $2^{90}-1$.