Time complexity of algorithms 7^logn

Question

I have a question regarding time complexity. Is the time complexity of 7^logn in Θ(n) or Θ(n^n) or Θ(n^2) or something complety different? It confuses because the n is in the exponent. Thank you for your help

Answer 1

You can use a few logarithmic identities :

7^log(n) = 7^(log_7(n)/log_7(2)) = n^(1/log_7(2)) = n^log(7) ~= n^2.8

Answer 2

I think you can look on the following:

theta(n^2)=4^logn<7^logn<8^logn=2^3logn=theta(n^3)