$8.30 \log _{\frac{x-1}{x+5}} 0.3>0$.

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$8.30 \log _{\frac{x-1}{x+5}} 0.3>0$.
8.30 According to the condition, the logarithm of the number 0.3, which is less than 1, is positive. This can only be the case if the base of the logarithm is a positive number less than 1 (Fig. 8.13). Thus, we have the system of inequalities $0 < a < 1$.

Answer: $(1, \infty)$.

![](https://cdn.mathpix.com/cropped/2024_05_21_1e3d8d2f6605ac23e2a5g-279.jpg?height=465&width=446&top_left_y=904&top_left_x=377)

Fig. 8.13