$\begin{array}{l}a)\,\,3^{2x+1}.7^y=9.21^x\\\Leftrightarrow 3^{2x+1}.7^y=3^2.(3.7)^x\\\Leftrightarrow 3^{2x+1}.7^y=3^2.3^x.7^x\\\Leftrightarrow 3^{2x+1}.7^y=3^{2+x}.7^x \\\Leftrightarrow \begin{cases} 3^{2x+1}=3^{2+x}\\7^y=7^x\end{cases}\\\Leftrightarrow \begin{cases} 2x+1=2+x\\y=x\end{cases}\\\Leftrightarrow \begin{cases}2x-x=2-1\\y=x\end{cases}\\\Leftrightarrow \begin{cases}x=1\\y=x\end{cases} \\\Leftrightarrow \begin{cases} x=1\\y=1\end{cases}\\\text{- Vậy cặp số $(x,y)$ thỏa mãn là $(1,1)$}\\\,\\b)\,\,\text{- Ta có :}\\\dfrac{27^x}{3^{2x-y}}=243\\\Leftrightarrow \left(3^3\right)^x\div3^{2x-y}=243\\\Leftrightarrow 3^{3x}\div3^{2x-y}=243\\\Leftrightarrow 3^{3x-(2x-y)}=243\\\Leftrightarrow 3^{3x-2x+y}=243\\\Leftrightarrow 3^{x+y}=243\\\Leftrightarrow 3^{x+y}=3^5\\\Leftrightarrow x+y=5\,\,\quad(1)\\\text{- Ta lại có :}\\\dfrac{25^x}{5^{x+y}}=125\\\Leftrightarrow \left(5^2\right)^x\div5^{x+y}=125\\\Leftrightarrow 5^{2x}\div5^{x+y}=125\\\Leftrightarrow 5^{2x-(x+y)}=125\\\Leftrightarrow 5^{2x-x-y}=125\\\Leftrightarrow 5^{x-y}=125\\\Leftrightarrow 5^{x-y}=5^3\\\Leftrightarrow x-y=3\,\,\quad(2)\\\text{- Từ (1) và (2)}\Rightarrow \begin{cases} x=(5+3)\div2=4\\y=(5-3)\div2=1\end{cases}\\\text{- Vậy cặp số $(x,y)$ thỏa mãn là : $(4,1)$} \end{array}$
