Q:

Determine the number of digits in $(2^{120})(5^{125})$.

Determine the number of digits in $(2^{120})(5^{125})$.
This is a bonus question I found in a Grade 12 math textbook, and I'm curious on how to solve it. What I find strange is that this question is in the  "Power Functions" section of "Polynomial Functions"; yet, this seems to have little to do with functions.
Any ideas as to how to solve this? I have tried to, but can't find a solution without a computer or calculator.

A:

Observe that 
$$2^{120}5^{125}=2^{120}5^{120}5^5=10^{120}\cdot3125$$
So the number is $3125$ followed by $120$ zeroes.

