Вычислить (267-276). 267 1) log₂ 16; 2) log₂ 64; 3) log₂ 2; 4) log₂ 1. 268 1) log₂ 1/2; 2) log₂ 1/8; 3) log₂ √2; 4) log₂ 1/(4√2).

Решим каждое задание по порядку.

267)

1. $$log_2 16 = log_2 2^4 = 4$$
2. $$log_2 64 = log_2 2^6 = 6$$
3. $$log_2 2 = 1$$
4. $$log_2 1 = 0$$

268)

1. $$log_2 \frac{1}{2} = log_2 2^{-1} = -1$$
2. $$log_2 \frac{1}{8} = log_2 2^{-3} = -3$$
3. $$log_2 \sqrt{2} = log_2 2^{\frac{1}{2}} = \frac{1}{2}$$
4. $$log_2 \frac{1}{\sqrt[4]{2}} = log_2 2^{-\frac{1}{4}} = -\frac{1}{4}$$