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Dear Student,
Please find below the solution to the asked query:

We have, \log_{\frac{1}{3}} (\log_{4} (x^{2} - 5)) > 0 \Rightarrow \log_{4} (x^{2} - 5) < 0 (As, base is less than 1, so the sign gets changed) \Rightarrow (x^{2} - 5) < 0 (As, base is greater than 1, so the sign remained same) \Rightarrow (x + \sqrt{5}) (x - \sqrt{5}) < 0 \Rightarrow x \in (- \sqrt{5}, \sqrt{5})

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