8. Найдите значение х, если: a) $$\log_4 x = 3$$; б) $$\log_{\frac{1}{27}} x = 3$$; в) $$\log_2 x = 2 \log_2 3 + \frac{1}{2} \log_2 9 - \log_2 6$$

a) $$\log_4 x = 3$$ $$x = 4^3 = 64$$ б) $$\log_{\frac{1}{27}} x = 3$$ $$x = (\frac{1}{27})^3 = (\frac{1}{3^3})^3 = (3^{-3})^3 = 3^{-9} = \frac{1}{3^9} = \frac{1}{19683}$$ в) $$\log_2 x = 2 \log_2 3 + \frac{1}{2} \log_2 9 - \log_2 6$$ $$\log_2 x = \log_2 3^2 + \log_2 9^{\frac{1}{2}} - \log_2 6$$ $$\log_2 x = \log_2 9 + \log_2 3 - \log_2 6$$ $$\log_2 x = \log_2 \frac{9 \cdot 3}{6} = \log_2 \frac{27}{6} = \log_2 \frac{9}{2}$$ $$x = \frac{9}{2} = 4.5$$