第10章 10.6

(1)

$\log_2 3 \log_3 4 \log_4 5 \log_5 6 \log_6 7 \log_7 8 = \frac{1}{\log_3 2}\log_3 4 \cdot \frac{\log_3 5 \log_3 6 \log_3 7 \log_3 8}{\log_3 4 \log_3 5 \log_3 6 \log_3 7} = \frac{\log_3 8}{\log_3 2} = \frac{3\log_3 2}{\log_3 2} = 3$

(2)

$\log_2 27 \log_3 \frac{1}{2} \log_4 8 = \frac{\log_3 27}{\log_3 2}\log_3 2^{-1} \frac{\log_2 8}{\log_2 4} = \frac{3}{\log_3 2}(-\log_3 2)\frac{3}{2} = -\frac{9}{2}$