Answer
$x=-8$
Work Step by Step
$4^{x-1}=8^{x+2}$
Rewrite $4$ as $2^{2}$ and $8$ as $2^{3}$:
$(2^{2})^{x-1}=(2^{3})^{x+2}$
Multiply the exponents on both sides of the equation:
$2^{2x-2}=2^{3x+6}$
If $2^{2x-2}=2^{3x+6}$, then $2x-2=3x+6$:
$2x-2=3x+6$
Solve for $x$:
$2x-3x=6+2$
$-x=8$
$x=-8$
