How to calculate how many digits in a number from index notation

Question

How can you calculate how many digits are in a number from its index notation?

I need to calculate how many digits are in the number $2^{30} * 5^{25}$

Answer 1

$2^{30}\times5^{25} = 10^{25}\times2^{5} = 32 \times 10^{25}$

Edit

So, there are two digits for 32 and 25 zeros after it. 27 in total.

Answer 2

For your particular case, $2^{30} \cdot 5^{25} = 2^5\cdot 10^{25}$, which should be straightforward, given that $10^n$ is the smallest number with $n{+}1$ digits.