296 2) log714-1 3 log6 30-1 2 log7 56 log 6 150

$$\frac{log_7 14 - \frac{1}{3}log_7 56}{log_6 30 - \frac{1}{2}log_6 150} = \frac{log_7 14 - log_7 \sqrt[3]{56}}{log_6 30 - log_6 \sqrt{150}} = \frac{log_7(\frac{14}{\sqrt[3]{56}})}{log_6(\frac{30}{\sqrt{150}})} = \frac{log_7(\frac{14}{\sqrt[3]{8 \cdot 7}})}{log_6(\frac{30}{\sqrt{25 \cdot 6}})} = \frac{log_7(\frac{14}{2\sqrt[3]{7}})}{log_6(\frac{30}{5\sqrt{6}})} = \frac{log_7(\frac{7}{\sqrt[3]{7}})}{log_6(\frac{6}{\sqrt{6}})} = \frac{log_7(7^{\frac{2}{3}})}{log_6(6^{\frac{1}{2}})} = \frac{\frac{2}{3}log_7 7}{\frac{1}{2}log_6 6} = \frac{\frac{2}{3}}{\frac{1}{2}} = \frac{2}{3} \cdot 2 = \frac{4}{3}$$.

Ответ: 4/3