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If $4^{x} - 4^{x - 1} = 24$ , then $x$ is $\frac{m}{2}$ . The value of $m$ is

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Solution

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$4^{x} - 4^{x} \times 4^{- 1} = 24$
$\Rightarrow 4^{x} (1 - \frac{1}{4}) = 24$
$\Rightarrow 4^{x} (\frac{4 - 1}{4}) = 24$
$= 4^{x} = \frac{24 \times 4}{3}$
$\Rightarrow 4^{x} = 32$
$= 2^{2 x} = 2^{5}$
$\Rightarrow x = \frac{5}{2}$

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