296 2) \(\frac{\log_7 14 - \frac{1}{3} \log_7 56}{\log_6 30 - \frac{1}{2} \log_6 150}\)

Используем свойства логарифмов: \(c \log_a b = \log_a b^c\), \(\log_a b - \log_a c = \log_a \frac{b}{c}\) и \(\frac{\log_a b}{\log_a c} = \log_c b\). \(\frac{\log_7 14 - \frac{1}{3} \log_7 56}{\log_6 30 - \frac{1}{2} \log_6 150} = \frac{\log_7 14 - \log_7 \sqrt[3]{56}}{\log_6 30 - \log_6 \sqrt{150}} = \frac{\log_7 \frac{14}{\sqrt[3]{56}}}{\log_6 \frac{30}{\sqrt{150}}} = \frac{\log_7 \frac{14}{2\sqrt[3]{7}}}{\log_6 \frac{30}{5\sqrt{6}}} = \frac{\log_7 \frac{7}{\sqrt[3]{7}}}{\log_6 \frac{6}{\sqrt{6}}} = \frac{\log_7 7^{\frac{2}{3}}}{\log_6 6^{\frac{1}{2}}} = \frac{\frac{2}{3}}{\frac{1}{2}} = \frac{4}{3}\).
Ответ: 4/3