Solve for $x$ : $2^{3 x + 3} = 2^{3 x + 1} + 48$ .

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Solution

As given $\Rightarrow 2^{3 x + 3} = 2^{3 x + 1} + 48$
$\Rightarrow 2^{3 x + 3} - 2^{3 x + 1} = 48$
$\Rightarrow 2^{3 x} (2^{3} - 2^{1}) = 48$
$\Rightarrow 2^{3 x} (8 - 2) = 48$
$\Rightarrow 2^{3 x} (6) = 48$
$\Rightarrow 2^{3 x} = \frac{48}{6}$
$\Rightarrow 2^{3 x} = 8$
$\Rightarrow 2^{3 x} = 2^{3}$
Base are same so
$\Rightarrow 3 x = 3 \Rightarrow x = 1$

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