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a: \(\Leftrightarrow2^3< 2^x< 2^4\)
=>3<x<4
mà x là số nguyên
nên \(x\in\varnothing\)
b: \(\Leftrightarrow3^3< 3^{12-x}< 3^5\)
=>12-x=4
hay x=8
c: \(\Leftrightarrow\left(\dfrac{2}{5}\right)^x>\left(\dfrac{2}{5}\right)^3\cdot\left(\dfrac{2}{5}\right)^2=\left(\dfrac{2}{5}\right)^5\)
=>x>5
d: \(\Leftrightarrow3x-1=-4\)
=>3x=-3
hay x=-1
a: \(\Leftrightarrow2^3< 2^x< 2^4\)
=>3<x<4
mà x là số nguyên
nên \(x\in\varnothing\)
b: \(\Leftrightarrow3^3< 3^{12-x}< 3^5\)
=>12-x=4
hay x=8
c: \(\Leftrightarrow\left(\dfrac{2}{5}\right)^x>\left(\dfrac{2}{5}\right)^3\cdot\left(\dfrac{2}{5}\right)^2=\left(\dfrac{2}{5}\right)^5\)
=>x>5
d: \(\Leftrightarrow3x-1=-4\)
=>3x=-3
hay x=-1
a,9<3x<39.3-2
\(\Leftrightarrow3^2< 3< 3^7\)
\(\Rightarrow S=\left\{3;4;5;6\right\}\)
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) \(27< 81^3:3^x< 243\)
\(\Leftrightarrow3^2< \left(3^4\right)^3:3^x< 3^5\)
\(\Leftrightarrow3^2< 3^{12}:3^x< 3^5\)
\(\Leftrightarrow3^2< 3^{12-x}< 3^5\)
\(\Leftrightarrow2< 12-x< 5\)
\(\Leftrightarrow\hept{\begin{cases}x=8\\x=9\end{cases}}\)
\(a)8< 2^x\le2^9.2^{-5}\)
\(\Leftrightarrow2^3< 2^x\le2^9.\dfrac{1}{2^5}\)
\(\Leftrightarrow2^3< 2^x\le2^4\)
\(\Leftrightarrow x=4\)
\(b)27< 81^3:3^x< 243\)
\(\Leftrightarrow3^3< \left(3^4\right)^3:3^x< 3^5\)
\(\Leftrightarrow3^3< 3^{12}:3^x< 3^5\)
\(\Leftrightarrow3^3< 3^{12-x}< 3^5\)
\(\Leftrightarrow12-x=4\)
\(\Leftrightarrow x=8\)