CAT 2017 [slot 1] Question with solution 24

Question 24:
If $9^{2x-1}-81^{x-1}=1944$, then x is
  1. 3
  2. 9/4
  3. 4/9
  4. 1/3
Option: 2
Explanation:

$\frac{81^x}{9} - \frac{81^x}{81} = 1944$

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

$81^x × [\frac{8}{81}] = 243$

$3^{4x} = 3^9$

$x = \frac{9}{4}$

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