Вычислить: 1) log√3 1/(3*3^(1/3)); 2) log√5 1/(25*5^(1/4)); 3) 2^(2-log2 5); 4) 3,6^(log3,6 10 + 1); 5) 2*log5 √5 + 3*log2 8; 6) log2 log2 log2 2^16.

Давай решим эти примеры по порядку: 1) $\log_{\sqrt{3}} \frac{1}{3 \sqrt[3]{3}} = \log_{3^{1/2}} \frac{1}{3^1 \cdot 3^{1/3}} = \log_{3^{1/2}} \frac{1}{3^{4/3}} = \log_{3^{1/2}} 3^{-4/3} = \frac{-4/3}{1/2} = -\frac{4}{3} \cdot 2 = -\frac{8}{3} = -2\frac{2}{3}$. 2) $\log_{\sqrt{5}} \frac{1}{25 \sqrt[4]{5}} = \log_{5^{1/2}} \frac{1}{5^2 \cdot 5^{1/4}} = \log_{5^{1/2}} \frac{1}{5^{9/4}} = \log_{5^{1/2}} 5^{-9/4} = \frac{-9/4}{1/2} = -\frac{9}{4} \cdot 2 = -\frac{9}{2} = -4,5$. 3) $2^{2 - \log_2 5} = \frac{2^2}{2^{\log_2 5}} = \frac{4}{5} = 0,8$. 4) $3,6^{\log_{3,6} 10 + 1} = 3,6^{\log_{3,6} 10} \cdot 3,6^1 = 10 \cdot 3,6 = 36$. 5) $2 \log_5 \sqrt{5} + 3 \log_2 8 = 2 \log_5 5^{1/2} + 3 \log_2 2^3 = 2 \cdot \frac{1}{2} + 3 \cdot 3 = 1 + 9 = 10$. 6) $\log_2 \log_2 \log_2 2^{16} = \log_2 \log_2 16 = \log_2 4 = 2$.