AMC 12B 2024 (Problem 6)

The national debt of the United States is on track to reach

5\cdot10^{13}

dollars by 2033. How many digits does this number of dollars have when written as a numeral in base 5? (The approximation of

\log_{10}5

0.7

is sufficient for this problem.)

\text{(A)}\;18

\text{(B)}\;20

\text{(C)}\;22

\text{(D)}\;24

\text{(E)}\;26