Questions: Identifying a Graphical Solution Which graph shows the solution to the equation 4^(x-3)=8?

Identifying a Graphical Solution Which graph shows the solution to the equation 4^(x-3)=8?
Transcript text: Identifying a Graphical Solution Which graph shows the solution to the equation $4^{x-3}=8$ ?
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Solution

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Solution Steps

Step 1: Rewrite the equation

The given equation is $4^{x-3} = 8$. We can rewrite both sides of the equation as powers of 2: $4^{x-3} = (2^2)^{x-3} = 2^{2(x-3)} = 2^{2x-6}$ $8 = 2^3$ So, $2^{2x-6} = 2^3$.

Step 2: Solve for x

Since the bases are equal, the exponents must be equal as well: $2x - 6 = 3$ $2x = 3 + 6$ $2x = 9$ $x = \frac{9}{2} = 4.5$

Step 3: Identify the correct graph

The solution to the equation $4^{x-3}=8$ is $x = 4.5$. This solution represents the x-coordinate where the graphs of $y = 4^{x-3}$ and $y = 8$ intersect. The first graph shows the intersection at $x = 4.5$.

Final Answer

The first graph is the correct one.

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