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$\frac{81^x}{9} - \frac{81^x}{81} = 1944$
$81^x × [\frac{1}{9}- \frac{1}{81}] = 1944$
$81^x × [\frac{8}{81}] = 243$
$3^{4x} = 3^9$
$x = \frac{9}{4}$