2 log327 log121 log12144 log11 log1313 log4464 logs 125 log264 log15 225 4. logs 45 log143 196 log7349 log62216

Для решения данных логарифмических выражений необходимо воспользоваться свойствами логарифмов и степеней.

1. $$log_3 \sqrt[4]{27} = log_3 (3^3)^{\frac{1}{4}} = log_3 3^{\frac{3}{4}} = \frac{3}{4}$$
2. $$log_{11} \sqrt[3]{121} = log_{11} (11^2)^{\frac{1}{3}} = log_{11} 11^{\frac{2}{3}} = \frac{2}{3}$$
3. $$log_{12} \sqrt[3]{144} = log_{12} (12^2)^{\frac{1}{3}} = log_{12} (12 \cdot 12)^{\frac{1}{3}} = log_{12} (12^2)^{\frac{1}{3}} = \frac{2}{3} log_{12} 12 = \frac{2}{3}$$
4. $$log_{11} \sqrt[5]{11} = log_{11} 11^{\frac{1}{5}} = \frac{1}{5}$$
5. $$log_{13} \sqrt[3]{13} = log_{13} 13^{\frac{1}{3}} = \frac{1}{3}$$
6. $$log_4 \sqrt[4]{64} = log_4 (4^3)^{\frac{1}{4}} = log_4 4^{\frac{3}{4}} = \frac{3}{4}$$
7. $$log_5 \sqrt[4]{125} = log_5 (5^3)^{\frac{1}{4}} = log_5 5^{\frac{3}{4}} = \frac{3}{4}$$
8. $$log_2 \sqrt[7]{64} = log_2 (2^6)^{\frac{1}{7}} = log_2 2^{\frac{6}{7}} = \frac{6}{7}$$
9. $$log_{15} \sqrt[5]{225} = log_{15} (15^2)^{\frac{1}{5}} = log_{15} 15^{\frac{2}{5}} = \frac{2}{5}$$
10. $$log_5 \sqrt[4]{5} = log_5 5^{\frac{1}{4}} = \frac{1}{4}$$
11. $$log_{14} \sqrt[3]{196} = log_{14} (14^2)^{\frac{1}{3}} = log_{14} 14^{\frac{2}{3}} = \frac{2}{3}$$
12. $$log_7 \sqrt[3]{49} = log_7 (7^2)^{\frac{1}{3}} = log_7 7^{\frac{2}{3}} = \frac{2}{3}$$
13. $$log_6 \sqrt[2]{216} = log_6 (6^3)^{\frac{1}{2}} = log_6 6^{\frac{3}{2}} = \frac{3}{2}$$

Ответ: См. решения выше.