Question 61
a) Given that the decimal representation of $5^{2018}$ has 1411 digits and begins with 3 (the leftmost nonzero digit is 3), for how many integers $1 \leq n \leq 2017$ does the number $5^{n}$ begin with 1?
b) The integers $4^{52}$ and $5^{52}$ both begin with the digit 2. If the decimal representations of the powers $4^{n}$ and $5^{n}$, with $n\gt 0$ an integer, begin with the same digit $d$, what are the possible values of this digit?
b) The integers $4^{52}$ and $5^{52}$ both begin with the digit 2. If the decimal representations of the powers $4^{n}$ and $5^{n}$, with $n\gt 0$ an integer, begin with the same digit $d$, what are the possible values of this digit?