Question

Which graph shows the solution to the equation (see the attached photo)

Answer 1

Given: An equation

`4^(x-3)=8`

Required: To draw the graph of the solution of the equation.

Explanation: The given equation is-

`4^(x-3)=8`

Solving,

`\begin{gathered} (2^2)^(x-3)=2^3 \\ 2^(2x-6)=2^3 \end{gathered}`

Now since the base on both sides are the same hence the exponents must also be equal i.e.,

`\begin{gathered} 2x-6=3 \\ 2x=9 \\ \Rightarrow x=(9)/(2) \end{gathered}`

Hence the graph of the equation can be drawn by taking the equations

`\begin{gathered} y=4^(x-3) \\ y=8 \end{gathered}`

Hence the graph is

Final Answer: Option C is correct.