Question 24

If $$9^{2x-1}-81^{x-1}=1944$$, then $$x$$ is

Solution

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

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

$$81^x * [\frac{1}{81}] = 243$$

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

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

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