Question

Which of the numbers ${1000}^{1000},{1001}^{999}$ is greater?

Answer 1

$\log {1000}^{1000}=1000\log 1000=1000\times 3=3000$

$\log {1001}^{999}=999\log 1001=\left(999\right)\left(3.0004340\right)=3002.5651$

Hence, ${1001}^{999}>{1000}^{1000}$