13.376 The desired three-digit number ends with the digit 1. If it is erased and then written as the first digit of the number, the new three-digit number obtained will be less than the desired one by $10 a^{\log _{\sqrt{a}} 3}$. Find this number.
Solution. Let $\overline{x y 1}$ be the desired number. Then

$$
\begin{aligned}
& \overline{x y 1}-\overline{1 x y}=10 a^{\log _{\sqrt{a}} 3} \Leftrightarrow(100 x+10 y+1)-(100+10 x+y)=90 \Rightarrow \\
& \Rightarrow 10 x+y=21 \Leftrightarrow \overline{x y}=21 .
\end{aligned}
$$

Answer: 211 .