第10章 10.5

(1)

$\log_4 9 - \log_4 3 = \log_4 3^2 - \log_4 3 = 2\log_4 3 - \log_4 3 = \log_4 3$

(2)

$\log_5 81 - \log_5 9 = \log_5 3^4 - \log_5 3^2 = 4\log_5 3 - 2\log_5 3 = 2\log_5 3$

(3)

$\log_5 \sqrt{2} - \log_5 8 = \frac{1}{2}\log_5 2 - 3\log_5 2 = -\frac{5}{2}\log_5 2$

(4)

$\log_2 2^{-2} + \log_2 \sqrt[3]{2} = -2\log_2 2 + \frac{1}{3}\log_2 2 = -\frac{5}{3}\log_2 2 = -\frac{5}{3}$

(5)

$\log 50 - \log 100 = \log\left(\frac{50}{100}\right) = \log\left(\frac{1}{2}\right) = \log 2^{-1} = -\log 2$

(6)

$4\log\sqrt{150} - \log 54 + \log 24 = 2\log 150 - \log 54 + \log 24 = \log 150^2 - \log 54 + \log 24$

$= \log\left(\frac{150^2 \cdot 24}{54}\right) = \log(50 \cdot 50 \cdot 4) = \log 10^4 = 4$