\(4\cdot3^{x-2}+2\cdot3^{x+1}=4\cdot3^4+2\cdot3^7\)
=>\(4\cdot3^x\cdot\dfrac{1}{9}+2\cdot3^x\cdot3=3^4\left(4+2\cdot3^3\right)\)
=>\(3^x\left(\dfrac{4}{9}+6\right)=3^4\cdot\left(4+2\cdot3^3\right)\)
=>\(3^x\cdot\left(\dfrac{4}{9}+\dfrac{54}{9}\right)=3^4\cdot\left(4+2\cdot27\right)\)
=>\(3^x\cdot\dfrac{58}{9}=3^4\cdot58\)
=>\(\dfrac{3^x}{9}=3^4\)
=>x-2=4
=>x=6
\(4\cdot3^{x-2}+2\cdot3^{x+1}=4\cdot3^4+2\cdot3^7\\ 4\cdot3^{x-2}+2\cdot3^{x-2+3}=324+4374\\ 3^{x-2}\cdot\left(4+54\right)=4698\\ 3^{x-2}\cdot58=4698\\ 3^{x-2}=81\\ 3^x:3^2=81\\ 3^x=729=3^6\\ ⇒\: x=6\)
