Largest number among the given numbers How to find the largest number among the following numbers.
$(a)\;3^{210}$
$(b)\;7^{140}$
$(c)\;17^{105}$
$(d)\;31^{84}$
Any help will be greatly appreciated.

If you are allowed a calculator, take the logs and compute them.  $\log 3^{210}=210 \log 3$ and so on  
If you must do it by hand, you need to be clever.  To compare a and b, note that the exponents are both divisible by $70$, so you are comparing $(3^3)^{70}$ and $(7^2)^{70}$.  You may know $3^3$ and $7^2$, or they are not hard to compute.  Similar techniques will deal with the others.
