6) log√2 7√2 - log√2 14;

6) Используем свойство логарифмов: $$log_a b - log_a c = log_a \frac{b}{c}$$. Тогда

$$log_{\sqrt{2}} 7\sqrt{2} - log_{\sqrt{2}} 14 = log_{\sqrt{2}} \frac{7\sqrt{2}}{14} = log_{\sqrt{2}} \frac{\sqrt{2}}{2} = log_{\sqrt{2}} \frac{\sqrt{2}}{(\sqrt{2})^2} = log_{\sqrt{2}} \frac{1}{\sqrt{2}} = log_{\sqrt{2}} (\sqrt{2})^{-1} = -1$$.

Ответ: -1