Hey guys, i need to prove without using calculator that:
$\displaystyle 17 ^{14} >31^{11}$
Alternatively, if
$\displaystyle 16^{14}>32^{11}\Rightarrow\ 17^{14}>31^{11}$
$\displaystyle 16^{14}=16^3\left[16^{11}\right]=\left[2^4\right]^3\left[16^{11}\right]=2^{12}\left[16^{11}\right]$
$\displaystyle 32^{11}=2^{11}\left[16^{11}\right]$
$\displaystyle 2^{12}\left[16^{11}\right]>2^{11}\left[16^{11}\right]\Rightarrow\ 16^{14}>32^{11}\Rightarrow\ 17^{14}>31^{11}$