If $4^{x} - 4^{x - 1} = 24$ ,then find the value of $x$ ?

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Solution

$4^{x} - 4^{x - 1} = 24$
Taking $4^{x - 1}$ common from the LHS:
$4^{x - 1} (4 - 1) = 24 ⟹ 4^{x - 1} \cdot 3 = 24 ⟹ 4^{x - 1} = 8$
$2^{2 x - 2} = 2^{3} ⟹ 2 x - 2 = 3$
$⟹ 2 x = 5 ⟹ x = \frac{5}{2} = 2.5$

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