Answer
$x=-8$
Work Step by Step
We are given that $4^{x-1}=8^{x+2}$. Both of these numbers are powers of 2, so we can rewrite the equation as $(2^{2})^{x-1}=(2^{3})^{x+2}$.
This can be rewritten as $2^{2x-2}=2^{3x+6}$
From the uniqueness of $b^{x}$, we know that $b^{x}=b^{y}$ is equivalent to $x=y$ (when $b\gt0$ and $b\ne1$).
Therefore, $2x-2=3x+6$. To solve for x, subtract 6 from both sides.
$2x-8=3x$
Next, subtract 2x from both sides.
$x=-8$
