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Comparison of Quantities Using Exponents

If 2x-1+2x+...

Question

If $2^{x - 1} + 2^{x + 1} = 1280$ , then find the value of $x$ .

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Solution

$2^{x - 1} + 2^{x + 1} = 1280$
$2^{x} (\frac{1}{2} + 2) = 1280$
$2^{x} (\frac{5}{2}) = 1280$
$2^{x} = 512$
$2^{x} = 2^{9}$
$x = 9$ .

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