Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 72

\[\boxed{\mathbf{72}\mathbf{.}}\]

\[1)\ 3^{\sqrt{71}}\ или\ 3^{\sqrt{69}};\]

\[71 > 69;\]

\[\sqrt{71} > \sqrt{69};\]

\[3^{\sqrt{71}} > 3^{\sqrt{69}}.\]

\[2)\ \left( \frac{1}{3} \right)^{\sqrt{3}}\ или\ \left( \frac{1}{3} \right)^{\sqrt{2}};\]

\[3 > 2;\]

\[\sqrt{3} > \sqrt{2};\]

\[\left( \frac{1}{3} \right)^{\sqrt{3}} < \left( \frac{1}{3} \right)^{\sqrt{2}}.\]

\[3)\ 4^{- \sqrt{3}}\ или\ 4^{- \sqrt{2}};\]

\[3 > 2;\]

\[\sqrt{3} > \sqrt{2};\]

\[- \sqrt{3} < - \sqrt{2};\]

\[4^{- \sqrt{3}} < 4^{- \sqrt{2}}.\]

\[4)\ 2^{\sqrt{3}}\ или\ 2^{1,7};\]

\[300 > 289;\]

\[\sqrt{300} > 17;\]

\[\sqrt{3} > 1,7;\]

\[2^{\sqrt{3}} > 2^{1,7}.\]

\[5)\ \left( \frac{1}{2} \right)^{1,4}\ или\ \left( \frac{1}{2} \right)^{\sqrt{2}};\]

\[196 < 200;\]

\[14 < \sqrt{200};\]

\[1,4 < \sqrt{2};\]

\[\left( \frac{1}{2} \right)^{1,4} > \left( \frac{1}{2} \right)^{\sqrt{2}}.\]

\[6)\ \left( \frac{1}{9} \right)^{\pi}\ или\ \left( \frac{1}{9} \right)^{3,14};\]

\[\pi \approx 3,1415\ldots;\]

\[\pi > 3,14;\]

\[\left( \frac{1}{9} \right)^{\pi} < \left( \frac{1}{9} \right)^{3,14}.\]