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State True or False. $$\log_2 13$$ is irrational.
Correct Answer: True
Suppose $$\log_2 13 = \frac{p}{q}$$ with positive integers $$p$$, $$q$$. Then $$2^p = 13^q$$, but the left side is even and the right side is odd, a contradiction. So $$\log_2 13$$ is irrational and the statement is True.
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