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Solve the fol...

Question

Solve the following equations.
$l o g_{2} (4^{x} + 4) - l o g_{2} (2 x + 1 - 3) = 0.$

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Solution

we know $l o g a - l o g b = l o g (a / b)$

therefore ${log}_{2} 4^{x} + 4 - {log}_{2} (2 x + 1 - 3) = {log}_{2} \frac{4^{x} + 4}{2 x - 2}$ =0

therefore $4^{x} + 4 = 2 x - 2$

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

which doesn't not have any solution since exponential function rises rapidly

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