Question

$\text{Solve for}x\text{in the equation}$ $log\left[log\right(2+lo{g}_2(x+1)\left)\right]=0$

• A. $2^8-1$
• B. $2^8$
• C. $2^2-1$
• D. $3^8-1$

Answer 1

The correct option is A

$2^8-1$

Rewrite the equation as
$log\left[log\right(2+lo{g}_2(x+1)\left)\right]=log\left(1\right)$,
$[\text{since log(1) = 0]}$

$log(2+lo{g}_2(x+1\left)\right)=1$

$2+lo{g}_2(x+1)=10$

$lo{g}_2(x+1)=8$

$x+1=2^8$

$x=2^8-1$