$4 \cdot 52$ for some natural number $n, 2^{n}$ and $5^{n}$ have the same digit in their highest place, what is this digit?



Translating the text into English while preserving the original formatting and line breaks, the result is as follows:

$4 \cdot 52$ for some natural number $n, 2^{n}$ and $5^{n}$ have the same digit in their highest place, what is this digit?
[Solution] Let this number be $a$. Since
$$
2^{n} \cdot 5^{n}=10^{n} \text {, }
$$

we have $a^{2}<10<(a+1)^{2}$.
Thus, we get $\quad a=3$. (For example, $2^{5}=32,5^{5}=3125$ )