Compare big exponent numbers using logarithms and without logarithms It's from an exam problem mostly, however, I believe will help many others out here.
Problem #1 

Which one is bigger: $31^{11}$ OR $17^{14}$

Problem #2

Which one is bigger: $31^{11}$ OR $14^{14}$

My logarithmic way for first one: $31^{11}$ ? $17^{14} \rightarrow 31 ? \;17^{14/11} \rightarrow 31 ?\; (17\cdot17^{0.3}$).
So $31^{11}$ < $17^{14}$. However, the problem with this way is the $17^{0.3}$, which I can't calculate without a calculator.
So Problem #3

How $17^{0.3}$ can be calculated without a calculator (while assuming I've memorized the values of $\log 2,\log 3,\log 5$ and $\log 7$.)

Please mention if there's any general way to solve these problems, fast!
Thank you!

$31^{11} < 32^{11} = 2^{11} 16^{11} <  2^{12} 17^{11} = 16^{3} 17^{11} < 16^3 17 ^{11} < 17^{14}$.
