You can convert 1000 to hex and see how many digits that requires:
So every integer below 1000 needs up to 3 digits.
Alternatively, we know that
, and that 
requires 
digits in its hex representation (e.g. 
). Taking the logarithm, we get 
, and adding 1 gives the number of digits needed to represent 
. Similarly,
So every integer below 1000 needs up to 3 digits.
Alternatively, we know that