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a,\(8< 2^x\le2^9.2^{-5}\)
\(2^3< 2^x\le2^4\)
\(\Rightarrow x=4\)
b, \(27< 81^3.3^x< 243\)
\(3^3< 3^{12-x}< 3^5\)
\(\Rightarrow3< 12-x< 5\)
12-x=4
x=8
c,\(\left(\frac{2}{5}\right)^x>\left(\frac{2}{5}\right)^3.\left(\frac{2}{5}\right)^2\)
\(\left(\frac{2}{5}\right)^x>\left(\frac{2}{5}\right)^5\)
\(\Rightarrow x>5\)
x=6;7;8........
a) \(8< 2^x\le2^9.2^{-5}\)
\(\Leftrightarrow2^3< x\le2^{9-5}\)
\(\Leftrightarrow2^3< 2^x\le2^4\)
\(\Leftrightarrow3< x\le4\Leftrightarrow x=4\)
b) \(27< 81^3:3^x< 243\)
\(\Leftrightarrow3^2< \left(3^4\right)^3:3^x< 3^5\)
\(\Leftrightarrow3^2< 3^{12}:3^x< 3^5\)
\(\Leftrightarrow3^2< 3^{12-x}< 3^5\)
\(\Leftrightarrow2< 12-x< 5\)
\(\Leftrightarrow\hept{\begin{cases}x=8\\x=9\end{cases}}\)
\(a)8< 2^x\le2^9.2^{-5}\)
\(\Leftrightarrow2^3< 2^x\le2^9.\dfrac{1}{2^5}\)
\(\Leftrightarrow2^3< 2^x\le2^4\)
\(\Leftrightarrow x=4\)
\(b)27< 81^3:3^x< 243\)
\(\Leftrightarrow3^3< \left(3^4\right)^3:3^x< 3^5\)
\(\Leftrightarrow3^3< 3^{12}:3^x< 3^5\)
\(\Leftrightarrow3^3< 3^{12-x}< 3^5\)
\(\Leftrightarrow12-x=4\)
\(\Leftrightarrow x=8\)
\(27< 3^x:81^3< 243\)
\(3^3< 3^x:\left(3^4\right)^3< 3^5\)
\(3^3< 3^x:3^{12}< 3^5\)
\(3^3< 3^{x-12}< 3^5\)
\(\Rightarrow3< x-12< 5\)
\(\Rightarrow3+12< x< 5+12\)
\(\Rightarrow15< x< 17\)
\(\Rightarrow x=16\)