This paper focuses on the secondary network throughput scaling in cognitive radio networks when secondary users' transmission powers are optimally allocated. Throughput scaling laws are obtained for two different cognitive radio networks under two different communication scenarios. In the first network type called power-interference limited networks, secondary users' transmission powers are limited by both individual average power constraints and the constraint on the average interference that they cause to primary users. In the second network type called interference limited networks, secondary users' transmission powers are only limited by average interference constraint. For both network types, an asymmetric communication scenario, in which the channels between secondary users and the secondary base station experience Rayleigh fading and those between secondary users and the primary base station experience Rician fading, and a symmetric communication scenario, in which both types of channels experience Rayleigh fading, are considered. It is shown that the secondary network throughput scales like log log (K+1/eK N) and log (K+1/eK N) for power-interference limited and interference limited networks, respectively, under the asymmetric communication scenario, where N is the number of secondary users and K > 0 is the Rician factor. For the symmetric communication scenario, these scaling laws are given by log log (N) and log(N) for power-interference limited and interference limited networks, respectively.