Not sure how to give a hint without blatantly giving the answer but...
Consider an n - digit number in base b.
That is N=an−1an−2.....a0=∑k=0akbk N = a n − 1 a n − 2 . . . . . a 0 = ∑ k = 0 a k b k Note aka k < b so we can easily show NN < b n (may have to repeat and argue inductively.
And presumably to be n - digit than an−1≠0 a n − 1 ≠ 0 so N≥bn−1 N ≥ b n − 1 .
So we have: every n digit number is between bn−1 b n − 1 inclusively and bn b n exclusively. This should be blindingly obvious to us if b=10 b = 10 .
So... that's a really important and fundamental result. Remember and use it.
