I would like to calculate the number of digits of these multiplications

2 x 4

200 x 300

2 (12321) (1000).

I don't exactly know how to start. Of course I know that I can multiply the numbers and count the digits,

2 x 4 = 8 (1 digit)

200 x 300 = 60,000 (5 digits)

2 (12321) (1000) = 24,642,008 (8 digits).

But If the numbers are very large, it would be difficult to make this procedure, so I was maybe looking for another way (This is why I asked myself the question in the first place).