Вычислить: 1) log2 24 - 1/2 log2 72 / log3 18 - 1/3 log3 72

1) $\frac{\log_2 24 - \frac{1}{2} \log_2 72}{\log_3 18 - \frac{1}{3} \log_3 72} = \frac{\log_2 24 - \log_2 72^{1/2}}{\log_3 18 - \log_3 72^{1/3}} = \frac{\log_2 24 - \log_2 \sqrt{72}}{\log_3 18 - \log_3 \sqrt[3]{72}} = \frac{\log_2 \frac{24}{\sqrt{36 \cdot 2}}}{\log_3 \frac{18}{\sqrt[3]{8 \cdot 9}}} = \frac{\log_2 \frac{24}{6\sqrt{2}}}{\log_3 \frac{18}{2\sqrt[3]{9}}} = \frac{\log_2 \frac{4}{\sqrt{2}}}{\log_3 \frac{9}{\sqrt[3]{9}}} = \frac{\log_2 \frac{2^2}{2^{1/2}}}{\log_3 \frac{3^2}{3^{2/3}}} = \frac{\log_2 2^{3/2}}{\log_3 3^{4/3}} = \frac{3/2}{4/3} = \frac{3}{2} \cdot \frac{3}{4} = \frac{9}{8} = 1,125$ 2) $\frac{\log_7 14 - \frac{1}{3} \log_7 56}{\log_6 30 - \frac{1}{2} \log_6 150} = \frac{\log_7 14 - \log_7 \sqrt[3]{56}}{\log_6 30 - \log_6 \sqrt{150}} = \frac{\log_7 \frac{14}{\sqrt[3]{8 \cdot 7}}}{\log_6 \frac{30}{\sqrt{25 \cdot 6}}} = \frac{\log_7 \frac{14}{2\sqrt[3]{7}}}{\log_6 \frac{30}{5\sqrt{6}}} = \frac{\log_7 \frac{7}{\sqrt[3]{7}}}{\log_6 \frac{6}{\sqrt{6}}} = \frac{\log_7 7^{2/3}}{\log_6 6^{1/2}} = \frac{2/3}{1/2} = \frac{2}{3} \cdot 2 = \frac{4}{3} = 1,333...$ 3) $\frac{\log_2 4 + \log_2 \sqrt{10}}{\log_2 20 + 3 \log_2 2} = \frac{\log_2 (4 \cdot \sqrt{10})}{\log_2 (20 \cdot 2^3)} = \frac{\log_2 (4 \cdot \sqrt{10})}{\log_2 (20 \cdot 8)} = \frac{\log_2 (2^2 \cdot 10^{1/2})}{\log_2 160} = \frac{\log_2 (4 \cdot 10^{1/2})}{\log_2 (32 \cdot 5)} = \frac{\log_2 4 + \log_2 10^{1/2}}{\log_2 32 + \log_2 5} = \frac{2 + \frac{1}{2}\log_2 10}{5 + \log_2 5} = \frac{2 + \frac{1}{2}(\log_2 2 + \log_2 5)}{5 + \log_2 5} = \frac{2 + 0,5 + 0,5\log_2 5}{5 + \log_2 5} = \frac{2,5 + 0,5\log_2 5}{5 + \log_2 5} = \frac{0,5(5 + \log_2 5)}{5 + \log_2 5} = 0,5$ 4) $\frac{3 \log_7 2 - \frac{1}{2} \log_7 64}{4 \log_5 2 + \frac{1}{3} \log_5 27} = \frac{\log_7 2^3 - \log_7 64^{1/2}}{\log_5 2^4 + \log_5 27^{1/3}} = \frac{\log_7 8 - \log_7 8}{\log_5 16 + \log_5 3} = \frac{0}{\log_5 48} = 0$