[tex]3^x-1=0\\
3^x=1\\
x=0\\\\
3^x-9=0\\
3^x=9\\
x=2\\\\
1.\ x\in(-\infty,0]\\
-3^x+1+(-3^x+9)=8\\
-3^x-3^x+9=7\\
-2\cdot3^x=-2\\
3^x=1\\
\underline{x=0}\\\\
2.\ x\in(0,2]\\
3^x-1+(-3^x+9)=8\\
3^x-3^x+9=9\\
0=0\\
\underline{x\in(0,2]}\\\\
3.\ x\in(2,\infty)\\
3^x-1+3^x-9=8\\
2\cdot3^x=18\\
3^x=9\\
x=2\not \in (2,\infty)
[/tex]
[tex]\underline{x\in\emptyset}\\\\
x=0 \wedge x\in(0,2]\\
\boxed{x\in[0,2]}[/tex]
