第10章 10.9

(1)

$\log 6 = \log 2 + \log 3 = 0.3010 + 0.4771 = 0.7781$

(2)

$\log 5 = \log 10 - \log 2 = 1 - 0.3010 = 0.6990$

(3)

$\log 1.5 = \log 3 - \log 2 = 0.4771 - 0.3010 = 0.1761$

(4)

$\log 25 = \log 5 + \log 5 = 0.6990 + 0.6990 = 1.3980$

(5)

$\log \frac{2}{3} = \log 2 - \log 3 = 0.3010 - 0.4771 = -0.1761$

(6)

$\log \frac{1}{\sqrt{3}} = -\frac{1}{2}\log 3 = -\frac{1}{2} \cdot 0.4771 = -0.2386$

(7)

$\log 0.027 = \log 27 - \log 1000 = 3\log 3 - 3 = 3 \cdot 0.4771 - 3 = -1.5687$

(8)

$\log_2 3 = \frac{\log_{10} 3}{\log_{10} 2} = \frac{0.4771}{0.3010} = 1.5850$

(9)

$\log_{18} 8 = \frac{\log_{10} 8}{\log_{10} 18} = \frac{3\log 2}{\log 2 + \log 3 + \log 3} = \frac{3 \cdot 0.3010}{0.3010 + 0.4771 + 0.4771} = 0.7194$