Question

корни степени логарифмы, решите прошу​

Answer 1

Ответ:

$(\frac{2}{3})^{\sqrt{3}} < (\frac{2}{3})^{-\pi}$

$(\frac{3}{2})^{\frac{5}{11}} > (\frac{3}{2})^{\frac{1}{3}}$

Пошаговое объяснение:

$(\frac{2}{3})^{\sqrt{3}}\; \; \; \; \; \; \;(\frac{2}{3})^{-\pi}=(\frac{3}{2})^{\pi}\\\\\frac{2}{3} < \frac{3}{2}\; \; = > \; \;(\frac{2}{3})^{\sqrt{3}}\ < (\frac{3}{2})^{\pi}\; \; = > \; \; (\frac{2}{3})^{\sqrt{3}} < (\frac{2}{3})^{-\pi}$

$(\frac{3}{2})^{\frac{5}{11}}\; \; \; \; \; (\frac{3}{2})^{\frac{1}{3}}\\\\\frac{3}{2}=1\frac{1}{2} > 1\\\\\frac{5}{11}=\frac{5*3}{11*3}=\frac{15}{33}\\\\\frac{1}{3}=\frac{1*11}{3*11}=\frac{11}{33}\\\\15 > 11\; \; = > \frac{15}{33} > \frac{11}{33}\; \; = > \; \; (\frac{3}{2})^{\frac{5}{11}} > (\frac{3}{2})^{\frac{1}{3}}$