a) \(36< 6^x\le7776\)
\(\Rightarrow6^2< 6^x\le6^5\)
\(\Rightarrow2< x\le5\)
\(\Rightarrow x\in\left\{3;4;5\right\}\)
b) \(\dfrac{2}{3}\cdot\left(\dfrac{8}{27}\right)\ge\left(\dfrac{2}{3}\right)^x\ge1\)
\(\Rightarrow\dfrac{2}{3}\cdot\left(\dfrac{2}{3}\right)^3\ge\left(\dfrac{2}{3}\right)^x\ge\left(\dfrac{2}{3}\right)^0\)
\(\Rightarrow\left(\dfrac{2}{3}\right)^4\ge\left(\dfrac{2}{3}\right)^x\ge\left(\dfrac{2}{3}\right)^0\)
\(\Rightarrow4\ge x\ge0\)
\(\Rightarrow x\in\left\{0;1;2;3;4\right\}\)
\(a,36< 6^x\le7776\)
\(\Rightarrow6^2< 6^x\le6^5\)
\(\Rightarrow2< x\le5\)
\(\Rightarrow x\in\left\{3;4;5\right\}\) (vì \(x\in N\))
Vậy: \(x\in\left\{3;4;5\right\}\).
\(---\)
\(b,\dfrac{2}{3}\cdot\left(\dfrac{8}{27}\right)\ge\left(\dfrac{2}{3}\right)^x\ge1\)
\(\Rightarrow1\le\left(\dfrac{2}{3}\right)^x\le\dfrac{2}{3}\cdot\dfrac{2^3}{3^3}\)
\(\Rightarrow\left(\dfrac{2}{3}\right)^0\le\left(\dfrac{2}{3}\right)^x\le\dfrac{2}{3}\cdot\left(\dfrac{2}{3}\right)^3\)
\(\Rightarrow\left(\dfrac{2}{3}\right)^0\le\left(\dfrac{2}{3}\right)^x\le\left(\dfrac{2}{3}\right)^4\)
\(\Rightarrow0\le x\le4\)
\(\Rightarrow x\in\left\{0;1;2;3;4\right\}\) (vì \(x\in N\))
Vậy: \(x\in\left\{0;1;2;3;4\right\}\)
#\(Toru\)
