If $2^{x-3}=4^2$, find $x$.
Since $4=2^2$, we have that $4^2={2^2}^2=2^4$. We know that $2^{x-3}=4^2=2^4$, so $x-3=4$. Solving for $x$, we find that $x=4+3=\boxed{7}$.
7
Level 2
Algebra
Problem: If $2^{x-3}=4^2$, find $x$.
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To solve the equation $2^{x-3}=4^2$, first recognize that $4$ can be expressed as a power of $2$. Specifically, $4 = 2^2$. Therefore, $4^2$ can be rewritten as $(2^2)^2$. Using the power of a power property, this simplifies to $2^{2 \cdot 2} = 2^4$. 

Now, the equation can be rewritten as $2^{x-3} = 2^4$. Since the bases are the same, we can set the exponents equal to each other. This gives us the equation $x - 3 = 4$. 

Next, solve for $x$ by adding $3$ to both sides of the equation: $x = 4 + 3$. 

Thus, $x = 7$. 

The final answer is $7$.<|END_OF_LATENT|> The final answer is $7$.