384 Вычислить: 2) log√5 1 / 4√5 ; 4) 3,6 log 3,6 10 + 1; 6) log₂ log₂ log₂ 2¹⁶.

2) $$log_{\sqrt{5}} \frac{1}{4 \sqrt{5}} = log_{\sqrt{5}} (4 \sqrt{5})^{-1} = -log_{\sqrt{5}} (4 \cdot 5^{1/2}) = -log_{\sqrt{5}} 4 - log_{\sqrt{5}} 5^{1/2} = -log_{\sqrt{5}} 2^2 - \frac{1}{2} log_{\sqrt{5}} 5 = -2 log_{\sqrt{5}} 2 - \frac{1}{2} log_{\sqrt{5}} (\sqrt{5})^2 = -2 log_{\sqrt{5}} 2 - \frac{1}{2} \cdot 2 = -2 log_{\sqrt{5}} 2 - 1$$

4) $$3,6^{log_{3,6} 10 + 1} = 3,6^{log_{3,6} 10} \cdot 3,6^1 = 10 \cdot 3,6 = 36$$

6) $$log_2 log_2 log_2 2^{16} = log_2 log_2 (16 log_2 2) = log_2 log_2 16 = log_2 log_2 2^4 = log_2 (4 log_2 2) = log_2 4 = log_2 2^2 = 2$$

Ответ: 2) -2log√5 2 - 1; 4) 36; 6) 2