$Solve for x in the equation$ $l o g [l o g (2 + l o g_{2} (x + 1))] = 0$

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Solution

Rewrite the equation as
$l o g [l o g (2 + l o g_{2} (x + 1))] = l o g (1)$ ,
$[since log(1) = 0]$

$l o g (2 + l o g_{2} (x + 1)) = 1$

$2 + l o g_{2} (x + 1) = 10$

$l o g_{2} (x + 1) = 8$

$x + 1 = 2^{8}$

$x = 2^{8} - 1$

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