第10章 10.4

(1)

$\log_a 49 = 2 \quad a^2 = 49 = 7^2 \quad a = 7$

(2)

$\log_a 4 = \frac{2}{3} \quad a^{\frac{2}{3}} = 4 = 2^2 = 2^{\frac{2}{3}\cdot 3} \quad a = 2^3 = 8$

(3)

$\log_a 4 = -\frac{1}{3} \quad a^{-\frac{1}{3}} = 4 = 2^2 = 2^{-\frac{1}{3}\cdot(-6)} \quad a = 2^{-6} = \frac{1}{64}$

(4)

$\log_a 27 = 0.75 \quad a^{\frac{3}{4}} = 27 = 3^3 = 3^{\frac{3}{4}\cdot 4} \quad a = 3^4 = 81$

(5)

$\log_a 9 = -\frac{1}{4} \quad a^{-\frac{1}{4}} = 9 = 9^{-\frac{1}{4}\cdot(-4)} \quad a = 9^{-4} = \frac{1}{6561}$

(6)

$\log_a \sqrt[4]{2} = \frac{1}{3} \quad a^{\frac{1}{3}} = \sqrt[4]{2} = 2^{\frac{1}{4}} = 2^{\frac{1}{3}\cdot\frac{3}{4}} \quad a = 2^{\frac{3}{4}}$