Question

Which one is greater between ${31}^{14}$ and ${17}^{18}$?

Answer 1

$Weknowthat32>31\to {\left(2\right)}^5>31Raisingbothsidestopowerof14\therefore {\left({\left(2\right)}^5\right)}^{14}>{31}^{14}\to 2^{70}>{31}^{12}.....\left(1\right)Nowconsider17>16\to 17>{\left(2\right)}^{4}Raisingbothsidestopowerof18\therefore {17}^{18}>{\left({\left(2\right)}^4\right)}^{18}\to {17}^{18}>2^{72}.....\left(2\right)Now{2}^{72}>2^{70}....\left(3\right)Frompoints1,2and3{17}^{18}>{31}^{14}$