1. Solving for unknown

solve for x in $
2^{x+1}-24\sqrt{2^x}+64=0
$

2. Originally Posted by Punch
solve for x in $
2^{x+1}-24\sqrt{2^x}+64=0
$
the easiest way is to let 2^x be an unknown, then factorise the equation and replace the solutions back with 2^x.

3. Originally Posted by Punch
solve for x in $
2^{x+1}-24\sqrt{2^x}+64=0
$
$2^{x+1}-24\sqrt{2^x}+64=0$

$2\cdot2^x-24\cdot2^{\frac{x}{2}}+64=0$

Let $y=2^{\frac{x}{2}}$

$2y^2-24y+64=0$

Solve the quadratic for $y$, then go back and find $x$.