If $9^{2x-1}-81^{x-1}=1944$, then $x$ is
$\frac{81^x}{9} - \frac{81^x}{81} = 1944$
$81^x * [\frac{1}{9}- \frac{1}{81}] = 1944$
$81^x * [\frac{1}{81}] = 243$
$3^{4x} = 3^9$
$x = \frac{9}{4}$
