Решыть

Ответ:

1. \(\log_{64}4=\dfrac13,\qquad \dfrac{\log_9 16}{\log_9 4}=2,\qquad \log_{\sqrt5}\sqrt{125}=3.\)

2. \[ \log_3\frac{5a^3b^4c}{3x^3y} =\log_3 5+3\log_3 a+4\log_3 b+\log_3 c-1-3\log_3 x-\log_3 y. \]

3. \[ \frac12\log_5 x-4\log_5 y+\frac25\log_5 z-3\log_5 t =\log_5\frac{x^{1/2}z^{2/5}}{y^4t^3}. \]