The algorithm needs to complete its task assuming the are n

$$pieces of input.

Four algorithms for doing the same task have complexities of A: n$^6/6,$ B: n$lo{g}_6$n$,$ C: n$(lo{g}_6$n$)^2,$ and D: $\sqrt[6]{n}lo{g}_{6}n.$

Rank the algorithms $in$ order $of$ increasing efficiency for large values $ofn.If$ you are comparing two algorithms where the first algorithm take more time $to$ complete the same task $(more$ operations $asn$ increases$)$ than the second algorithm, then the second $is$ more efficient. Show your work.