Find the value of $x$ , if $8^{255} = (32)^{x}$ .

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Solution

$8^{255} = (32)^{x}$
$\Rightarrow (2^{3})^{255} = (2^{5})^{x}$
$\Rightarrow (2)^{765} = (2)^{5 x}$
$\Rightarrow 5 x = 765$
$\Rightarrow x = 153$

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