ответ

To solve the expression given, use the properties of logarithms:

1. \(\log_b(m) - \log_b(n) = \log_b\left(\frac{m}{n}\right)\).

So the expression

\[ \frac{\log_7 8}{\log_7 15 - \log_7 30} \]

can be simplified as:

\[ \frac{\log_7 8}{\log_7\left(\frac{15}{30}\right)} \]

\[ = \frac{\log_7 8}{\log_7\left(\frac{1}{2}\right)} \]

Now, use the property \(\log_b(a^n) = n \log_b(a)\):

\[ = \frac{\log_7 8}{-1 \cdot \log_7 2} \]

\[ = -\frac{\log_7 8}{\log_7 2} \]

Finally, use the property \(\log_b(m^n) = n \log_b(m)\):

\[ = -\log_7(2^3) \]

\[ = -3 \log_7 2 \]

\[ = -3 \]