Given: An equation
[tex]4^{x-3}=8[/tex]
Required: To draw the graph of the solution of the equation.
Explanation: The given equation is-
[tex]4^{x-3}=8[/tex]
Solving,
[tex]\begin{gathered} (2^2)^{x-3}=2^3 \\ 2^{2x-6}=2^3 \end{gathered}[/tex]
Now since the base on both sides are the same hence the exponents must also be equal i.e.,
[tex]\begin{gathered} 2x-6=3 \\ 2x=9 \\ \Rightarrow x=\frac{9}{2} \end{gathered}[/tex]
Hence the graph of the equation can be drawn by taking the equations
[tex]\begin{gathered} y=4^{x-3} \\ y=8 \end{gathered}[/tex]
Hence the graph is
Final Answer: Option C is correct.
