第10章 10.7

(1)

$2^{\frac{1}{2}} = \sqrt{2} = 1.41421356$

$\log_{27} 3 = \frac{\log_3 3}{\log_3 27} = \frac{1}{3} = 3^{-1} = 0.3333$

$2^{-2} = \frac{1}{4} = 0.25$

$\log_{\frac{1}{2}} 2 = \frac{\log_2 2}{\log_2 \frac{1}{2}} = \frac{1}{-1} = -1$

これから

$2^{\frac{1}{2}} > \log_{27} 3 > 2^{-2} > \log_{\frac{1}{2}} 2$

(2)

$\log_2 3 = \log_2 \sqrt{9}$

$\frac{3}{2} = \frac{3}{2}\log_2 2 = \log_2 2^{\frac{3}{2}} = \log_2 \sqrt{8}$

$\frac{3}{2} = \frac{3}{2}\log_3 3 = \log_3 3^{\frac{3}{2}} = \log_3 \sqrt{27}$

$\log_9 25 = \frac{\log_3 25}{\log_3 9} = \frac{1}{2}\log_3 25 = \log_3 \sqrt{25}$

これから

$\log_2 3 > \frac{3}{2} > \log_9 25$