Answer
$x=-2$
Work Step by Step
$81^{x-1}=27^{2x}$
Rewrite $81$ as $3^{4}$ and $27$ as $3^{3}$:
$(3^{4})^{x-1}=(3^{3})^{2x}$
Transform this equation into $3^{4x-4}=3^{6x}$. This comes from multiplying the exponents on both sides of the equation:
$3^{4x-4}=3^{6x}$
If $3^{4x-4}=3^{6x}$, then $4x-4=6x$:
$4x-4=6x$
Solve for $x$:
$4x-6x=4$
$-2x=4$
$x=\dfrac{4}{-2}$
$x=-2$
