Work thus far: I know that in base ten to find the number of digits you just take the common log and round up, and I'm guessing that here you just take the log base nine of the number. I tried coming up with equations like $k\log_{9}27 = 9999$ meaning k = 6666 but I'm still kind of stuck and confused. Ans key says k is 19996/3, which is close to my answer.