we have the expression
[tex]\log _9(2x-7)=2x-3[/tex]applying property of log
we have
[tex]2x-7=9^{(2x-3)}[/tex]Verify
Apply log base 9 both sides
[tex]\begin{gathered} \log _9(2x-7)=\log _9(9^{(2x-3)}) \\ \log _9(2x-7)=(2x-3)\cdot\log _99 \\ \log _9(2x-7)=2x-3 \end{gathered}[/tex]