\(3^x+3^{x+2}=810\)
\(\Leftrightarrow3^x\left(1+3^2\right)=810\)
\(\Leftrightarrow3^x\left(1+9\right)=810\)
\(\Leftrightarrow3^x.10=810\)
\(\Leftrightarrow3^x=81\)
\(\Rightarrow x=4\)
3^x+3^x+2=810
<=>3^x(1+3^2)=810
<=>3^x(1+9)=810
<=>3^x 10=810
<=>3^x=810:10
<=>3^x=81
<=>x=4