The exponential equation is given to be:
[tex]9^{2x-1}=3^{-x+8}[/tex]
We can make the base of both sides be equal. We know that:
[tex]9=3^2[/tex]
Therefore, we have the equation become:
[tex]3^{2(2x-1)}=3^{-x+8}[/tex]
Since the bases are equal now, we can equate it and solve as shown below:
[tex]\begin{gathered} 2(2x-1)=-x+8 \\ 4x-2=-x+8 \\ 4x+x=8+2 \\ 5x=10 \\ x=\frac{10}{5} \\ x=2 \end{gathered}[/tex]
The correct answer is OPTION D.
