Answer
$x=-2$
Work Step by Step
We are given that $81^{x-1}=27^{2x}$. Both of these numbers are powers of 3, so we can rewrite the equation as $(3^{4})^{x-1}=(3^{3})^{2x}$.
Therefore,
$3^{4x-4}=3^{6x}$
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, $4x-4=6x$.
Subtract 4x from both sides.
$2x=-4$
Divide both sides by 2.
$x=-2$
