Number of Digits

$2^{10}=1024 \sim 10^{3}$ , this implies $2^{60} \sim 10^{18}$ and $2^{4}$ has two digits. Thus the only good option is $\boxed{20}$

$log({2}^{64})= 64 X log2 = 64 X 0.30103 =19.26592$

The integral part is 19, so no. of digits in ${2}^{64}$ is 19 + 1 =20

Take the log in the target base (10 ) of the number (264), drop the decimal portion, then add 1. $floor( log 2^64 ) + 1 = 20 digits.$

2^64 =1.~~~~~E19 by calculator..<..>19 + 1 =20