[tex]\displaystyle\\
E4.a) \\
3^{x+1}+3^x \ 108 \\
3^x\times 3^1+3^x \ 108 \\
3^x(3+1)=108\\
4\times 3^x = 108\\\\
3^x = \frac{108}{4}\\\\
3^x = 27 \\
3^x=3^3\\
\boxed{x=3}\\\\
E4.b)\\
3^{2x+1}+3^{2x}-3^{2x-1}=297\\
3^{2x-1+2}+3^{2x-1+1}-3^{2x-1}=297\\
3^{2x-1}\cdot 3^{2}+3^{2x-1}\cdot3^{1}-3^{2x-1}=297\\
3^{2x-1}(3^{2}+3^{1}-1)=297\\
3^{2x-1} \cdot 11 = 297\\ \\
3^{2x-1} = \frac{297}{11} \\ \\
3^{2x-1} =27\\
3^{2x-1} =3^3\\
2x+1 = 3\\
2x = 2\\\\
\boxed{x =1} [/tex]
[tex]\displaystyle\\
E4.c)\\
2^{x-2}+2^{x-3}+2^{x-4}=448\\
2^{x-4+2}+2^{x-4+1}+2^{x-4}=448\\
2^{x-4}\cdot 2^{2}+2^{x-4}\cdot 2^{1}+2^{x-4}=448\\
2^{x-4}(2^{2}+2^{1}+1)=448\\
2^{x-4}\cdot 7=448\\\\
2^{x-4} = \frac{448}{7} \\\\
2^{x-4} = 64\\
2^{x-4} = 2^6\\
x-4=6\\
x=6+4\\
\boxed{x=10}[/tex]
