The given equation is expressed as
[tex]\begin{gathered} 6^{3x}=6^{2x+7} \\ \text{The base is the same on both sides of the equation. Therefore, we would equate } \\ \text{the powers. It becomes} \\ 3x\text{ = 2x + 7} \\ 3x\text{ - 2x = 7} \\ x\text{ = 7} \end{gathered}[/tex]