Giải bài 84 trang 130 SGK giải tích nâng cao 12

a) ${{\left( \dfrac{2}{3} \right)}^{p}}>{{\left( \dfrac{3}{2} \right)}^{-q}}\Leftrightarrow {{\left( \dfrac{2}{3} \right)}^{p}}>{{\left( \dfrac{2}{3} \right)}^{q}}$

Vì $\dfrac{2}{3}<1\Rightarrow {{\left( \dfrac{2}{3} \right)}^{p}}>{{\left( \dfrac{2}{3} \right)}^{q}}\Leftrightarrow p< q$

b) ${{\left( \dfrac{8}{3} \right)}^{-p}}<{{\left( \dfrac{3}{8} \right)}^{q}}\Leftrightarrow {{\left( \dfrac{3}{8} \right)}^{p}}<{{\left( \dfrac{3}{8} \right)}^{q}}$

Vì $\dfrac{3}{8}<1\Rightarrow {{\left( \dfrac{3}{8} \right)}^{p}}<{{\left( \dfrac{3}{8} \right)}^{q}}\Leftrightarrow p>q$

c) $0,{{25}^{p}}<{{\left( \dfrac{1}{2} \right)}^{2q}}\Leftrightarrow {{\left( \dfrac{1}{4} \right)}^{p}}<{{\left( \dfrac{1}{4} \right)}^{q}}$

Vì $\dfrac{1}{4}<1\Rightarrow {{\left( \dfrac{1}{4} \right)}^{p}}<{{\left( \dfrac{1}{4} \right)}^{q}}\Leftrightarrow p>q$

d) ${{\left( \dfrac{7}{2} \right)}^{p}}<{{\left( \dfrac{2}{7} \right)}^{p-2q}}\Leftrightarrow {{\left( \dfrac{7}{2} \right)}^{p}}<{{\left( \dfrac{7}{2} \right)}^{2q-p}}$

Vì $\dfrac{7}{2}>1\Rightarrow {{\left( \dfrac{7}{2} \right)}^{p}}<{{\left( \dfrac{7}{2} \right)}^{2q-p}}\Leftrightarrow p<2q-p\Leftrightarrow p< q$