If $2^8=16^x$, find $x$.
We can write $16$ as $2^4$. Therefore, we can write our equation as $2^8 = 2^{4 \cdot x}$. Solving, we get that $x = \boxed{2}$.
2
Level 1
Algebra
Problem: If $2^8=16^x$, find $x$.
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To solve the equation $2^8 = 16^x$, we first need to express $16$ in terms of base $2$. We know that $16$ can be rewritten as $2^4$. Therefore, we can substitute $16$ in the equation:

$16^x = (2^4)^x$.

Using the power of a power property of exponents, we simplify this to:

$(2^4)^x = 2^{4x}$.

Now, we can rewrite the original equation with this substitution:

$2^8 = 2^{4x}$.

Since the bases are the same, we can set the exponents equal to each other:

$8 = 4x$.

Next, we solve for $x$ by dividing both sides of the equation by $4$:

$x = \frac{8}{4}$.

This simplifies to:

$x = 2$.

Thus, the final answer is $2$.<|END_OF_LATENT|> The final answer is $2$.