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In this paper, we analyze the allowable transmission power of cognitive radios when used as secondary users in a dynamic spectrum access network. Closed-form upper and lower bounds are derived, while accurate solutions to transmission power are available through numerical evaluation. The transmission power depends on the distance between primary and secondary transmitters as well as the number of randomly distributed primary receivers. The results show that at the cost of a small SINR redundancy of primary users, cognitive radios can use a significant level of transmission power in certain conditions.