a) \(125\le5^x< 625:\dfrac{1}{5^2}\)
\(\Rightarrow5^3\le5^x< 5^4\cdot5^2\)
\(\Rightarrow5^3\le5^x< 5^6\)
\(\Rightarrow3\le x< 6\)
\(\Rightarrow x\in\left\{3;4;5\right\}\)
b) \(\left(-\dfrac{32}{243}\right)\cdot\left(-\dfrac{8}{27}\right)\le\left(\dfrac{2}{3}\right)^x< 2022^0\)
\(\Rightarrow\left(-\dfrac{2}{3}\right)^5\cdot\left(-\dfrac{2}{3}\right)^3\le\left(\dfrac{2}{3}\right)^x< 1\)
\(\Rightarrow\left(-\dfrac{2}{3}\right)^8\le\left(\dfrac{2}{3}\right)^x< \left(\dfrac{2}{3}\right)^0\)
\(\Rightarrow\left(\dfrac{2}{3}\right)^8\le\left(\dfrac{2}{3}\right)^x< \left(\dfrac{2}{3}\right)^0\)
\(\Rightarrow8\le x< 0\)
\(\Rightarrow x\in\left\{1;2;3;4;5;6;7;8\right\}\)
