\(2\cdot3^{x+2}+4\cdot3^{x+1}=10\cdot3^6\)
\(2\cdot3^{x+1}\cdot3+4\cdot3^{x+1}=10\cdot3^6\)
\(\left(2\cdot3\right)\cdot3^{x+1}+4\cdot3^{x+1}=10\cdot3^6\)
\(6\cdot3^{x+1}+4\cdot3^{x+1}=10\cdot3^6\)
\(\left(6+4\right)\cdot3^{x+1}=10\cdot3^6\)
\(10\cdot3^{x+1}=10\cdot3^6\)
\(3^{x+1}=\left(10:10\right)\cdot3^6\)
\(3^{x+1}=3^6\)
`=>x+1=6`
`x=6-1`
`=>x-5`
`2.3^(x+2)+4.3^(x+1)=10.3^6`
`=> 2.(3^2).(3^x)+(4.3).(3^x)=10.3^6`
`=> 18.3^x+12.3^x=10.3.3^5`
`=> 3^x(18+12)=30.3^5`
`=> 3^x.30=30.3^5`
`=> x=5`
\(\Leftrightarrow2\cdot3^x\cdot9+4\cdot3^x\cdot3=10\cdot3^6\)
\(\Leftrightarrow3^x=10\cdot3^6:\left(2\cdot9+4\cdot3\right)=243\)
=>x=5
