\(4.3^{x+2}-3^{x-1}=963\)
\(\Rightarrow4.3^{x+2}-3^{x+2-3}=963\)
\(\Rightarrow4.3^{x+2}-\dfrac{1}{3^3}3^{x+2}=963\)
\(\Rightarrow4.3^{x+2}-\dfrac{1}{27}3^{x+2}=963\left(1\right)\)
Đặt \(t=3^{x+2}>0\)
\(\left(1\right)\Rightarrow4t-\dfrac{1}{27}t=963\)
\(\Rightarrow t\left(4-\dfrac{1}{27}\right)=963\)
\(\Rightarrow\dfrac{107}{27}.t=9.107\)
\(\Rightarrow t=3^2\Rightarrow t=3^2:\dfrac{1}{3^3}=3^2.\dfrac{3^3}{1}=3^5\)
\(\Rightarrow3^{x+2}=3^5\Rightarrow x+2=5\Rightarrow x=3\)
4\(\cdot\)3x+2-3x-1=963
=>4\(\cdot\)3xx32-3x:3=963
=>3x\(\cdot\)36-3x\(\cdot\)\(\dfrac{1}{3}\)=963
=>3x\(\cdot\)(36-\(\dfrac{1}{3}\))=963
=>3x\(\cdot\)\(\dfrac{107}{3}\)=963
=>3x=963:\(\dfrac{107}{3}\)=27=33
=>x=3
