3. Someone wrote down two numbers $5^{2020}$ and $2^{2020}$ in a row. How many digits will the resulting number contain?
Solution. Let the number $2^{2020}$ contain $m$ digits, and the number $5^{2020}$ contain $n$ digits. Then the following inequalities hold: $10^{m-1}<2^{2020}<10^{m}, 10^{n-1}<5^{2020}<10^{n}$ (the inequalities are strict because the power of two or five is not equal to the power of ten). Multiplying these inequalities, we get $10^{m+n-2}<10^{2020}<10^{m+n}$. From this, it follows that the exponent 2020 is between $m+n-2$ and $m+n$, so $2020=m+n-1$ and $m+n=2021$. This means that a total of 2021 digits have been written.

Answer: 2021.