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Product Law

Solve the fol...

Question

Solve the following equation for $x$ :

ii) $2^{x + 1} = 4^{x - 3}$

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Solution

$2^{x + 1} = 4^{x - 3}$

$\Rightarrow 2^{x + 1} = (2^{2})^{x - 3}$

$\Rightarrow 2^{x + 1} = 2^{2 (x - 3)}$ $[∵ (a^{m})^{n} = a^{m n}]$

$\Rightarrow 2^{x + 1} = 2^{2 x - 6}$

On comparing both sides, we get

$\Rightarrow x + 1 = 2 x - 6$

$\Rightarrow 2 x - x = 6 + 1$

$∴ x = 7$

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