1500. a) log 6-log 2√3; 6) log₁₂7√2 - log 14;

1500. Вычислите:

а) $$log_6 \sqrt{6} - log_6 2\sqrt{3} = log_6 \frac{\sqrt{6}}{2\sqrt{3}} = log_6 \frac{\sqrt{2}\sqrt{3}}{2\sqrt{3}} = log_6 \frac{\sqrt{2}}{2} = log_6 \frac{1}{\sqrt{2}} = log_6 2^{-\frac{1}{2}} = -\frac{1}{2} log_6 2$$

б) $$log_{\sqrt{12}} 7\sqrt{2} - log_{\sqrt{12}} 14 = log_{\sqrt{12}} \frac{7\sqrt{2}}{14} = log_{\sqrt{12}} \frac{\sqrt{2}}{2} = log_{\sqrt{12}} \frac{1}{\sqrt{2}} = log_{2^{2}3^{\frac{1}{2}}} 2^{-\frac{1}{2}} = -\frac{1}{2}log_{\sqrt{12}} 2$$

Ответ: a) $$\frac{-1}{2} log_6 2$$, б) $$\frac{-1}{2}log_{\sqrt{12}} 2$$