Chapter 4.1, Problem 12E

(a)

To determine

To prove: That $n-1=\lfloor {\log }_{b}N\rfloor$ (and hence that N has $1+\lfloor {\log }_{b}N\rfloor$ digits in base b), where natural number N is ${\left(a_{n-1}\mathrm{.....}{a}_0\right)}_b$ (in base b).

(b)

To determine

The number of digits in base 10 representation of $7^{254}$.

(c)

To determine

The number of digits in base 10 representation of ${319}^{566}$.