[tex]\bf 9^{2x+3}=27^{2x}\qquad
\begin{cases}
9=3^2\\
27=3^3
\end{cases}\implies (3^2)^{2x+3}=(3^3)^{2x}
\\\\\\
3^{2(2x+3)}=3^{3(2x)}\implies 3^{4x+6}=3^{6x}\impliedby
\begin{array}{llll}
\textit{base is the same, therefore,}\\
\textit{the exponents must}\\
\textit{ also be the same}
\end{array}
\\\\\\
4x+6=6x\implies 6=2x\implies \cfrac{6}{2}=x\implies 3=x[/tex]
