Bài tập 84 trang 130 SGK Toán 12 NC

a)

\(\begin{array}{l}
{\left( {\frac{2}{3}} \right)^p} > {\left( {\frac{3}{2}} \right)^{ - q}} \Leftrightarrow {\left( {\frac{2}{3}} \right)^p} > {\left( {\frac{2}{3}} \right)^q}\\
 \Leftrightarrow p < q\,\,\left( {\frac{2}{3} < 1} \right)
\end{array}\)

b)

\(\begin{array}{l}
{\left( {\frac{8}{3}} \right)^{ - p}} < {\left( {\frac{3}{8}} \right)^q} \Leftrightarrow {\left( {\frac{3}{8}} \right)^p} < {\left( {\frac{3}{8}} \right)^q}\\
 \Leftrightarrow p > q\,\,\left( {\frac{3}{8} < 1} \right)
\end{array}\)

c)

\(\begin{array}{l}
0,{25^p} < {\left( {\frac{1}{2}} \right)^{2q}} \Leftrightarrow {\left( {\frac{1}{4}} \right)^p} < {\left( {\frac{1}{4}} \right)^q}\\
 \Leftrightarrow p > q\,\,\left( {\frac{1}{4} < 1} \right)
\end{array}\)

d)

\(\begin{array}{l}
{\left( {\frac{7}{2}} \right)^p} < {\left( {\frac{2}{7}} \right)^{p - 2q}} \Leftrightarrow {\left( {\frac{7}{2}} \right)^p} < {\left( {\frac{7}{2}} \right)^{2q - p}}\\
 \Leftrightarrow p < 2q - p\,\,\left( {\frac{7}{2} > 1} \right)\\
 \Leftrightarrow 2p < 2q \Leftrightarrow p < q
\end{array}\)

-- Mod Toán 12 HỌC247