Since

      2N + 1 ~ 2N
   

this can be combined with the logarithm and then use the log properties to get a tilde approximation for

      log(2N + 1) ~ log(N)
   

like this:

(1) log(2N + 1) ~ log(2N) 

(2) log(2N) = log(2) + log(N) = 1 + log(N)

(3) 1 + log(N) ~ log(N)