266 Найти логарифмы чисел по основанию 3: 3, 9, 27, 81, 1, \frac{1}{3}, \frac{1}{9}, \frac{1}{243}, \sqrt[3]{3}, \frac{1}{3\sqrt{3}}, 9\sqrt[4]{3}.

Найдем логарифмы чисел по основанию 3:

1. $$log_3 3 = 1$$
2. $$log_3 9 = log_3 3^2 = 2$$
3. $$log_3 27 = log_3 3^3 = 3$$
4. $$log_3 81 = log_3 3^4 = 4$$
5. $$log_3 1 = 0$$
6. $$log_3 \frac{1}{3} = log_3 3^{-1} = -1$$
7. $$log_3 \frac{1}{9} = log_3 3^{-2} = -2$$
8. $$log_3 \frac{1}{243} = log_3 3^{-5} = -5$$
9. $$log_3 \sqrt[3]{3} = log_3 3^{\frac{1}{3}} = \frac{1}{3}$$
10. $$log_3 \frac{1}{3\sqrt{3}} = log_3 \frac{1}{3 \cdot 3^{\frac{1}{2}}} = log_3 \frac{1}{3^{\frac{3}{2}}} = log_3 3^{-\frac{3}{2}} = -\frac{3}{2} = -1.5$$
11. $$log_3 9\sqrt[4]{3} = log_3 (3^2 \cdot 3^{\frac{1}{4}}) = log_3 3^{\frac{9}{4}} = \frac{9}{4} = 2.25$$