Textbook Problem

Suppose a computer takes 1 nanosecond ( $={10}^{-9}$ second) to execute each operation. Approximately how long will it take the computer to execute the following numbers of operations? Convert your answers into seconds, minutes, hours, days, weeks, or years, as appropriate. For example, instead of $2^{50}$ nanoseconds, write 13 days.

a. ${\log }_{2}200$
b. $200$
c. $200{\log }_{2}200$
d. ${200}^2$
e. ${200}^8$
f. $2^{200}$