Which is the "fastest" paper-pencil method to compare (find which one is greater) $\sqrt[17]{6}$ and $\sqrt[16]{4}$?
My analysis bought this whole thing down to comparing which is greater between $6^{16}$ and $2^{34}$.Then by using the technique mention here doesn't gives the precise answer as $\log_2 6$ lies between $2 \text { and }3$, how else I could do this?