7.227. $(\lg (x+20)-\lg x) \log _{x} 0.1=-1$.
Solution.

Domain of definition: $\left\{\begin{array}{l}x+20>0, \\ 0<x \neq 1\end{array}\right.$ or $0<x \neq 1$.

Switch to base 10. We have $(\lg (x+20)-\lg x)\left(-\frac{1}{\lg x}\right)=-1 \Leftrightarrow$ $\Leftrightarrow \lg (x+20)-\lg x=\lg x \Leftrightarrow \lg (x+20)=2 \lg x \Leftrightarrow \lg (x+20)=\lg x^{2}$. Then $x+20=x^{2}, x^{2}-x-20=0$, from which $x_{1}=-4, x_{2}=5 ; x_{1}=-4$ does not satisfy the domain of definition.

Answer: 5.