solve for x in $\displaystyle 2^{x+1}-24\sqrt{2^x}+64=0 $
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Originally Posted by Punch solve for x in $\displaystyle 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.
Originally Posted by Punch solve for x in $\displaystyle 2^{x+1}-24\sqrt{2^x}+64=0 $ $\displaystyle 2^{x+1}-24\sqrt{2^x}+64=0$ $\displaystyle 2\cdot2^x-24\cdot2^{\frac{x}{2}}+64=0$ Let $\displaystyle y=2^{\frac{x}{2}}$ $\displaystyle 2y^2-24y+64=0$ Solve the quadratic for $\displaystyle y$, then go back and find $\displaystyle x$.
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