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Answer is given, and it equals to 1.

$ 2\cdot 16^{x}-2^{4x}-4^{2x-2}=15 $

$2^{4x-4}=-6,5$ <- This is where I reached, which is clearly wrong

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    @BeatShot: The edit had not shown up when I posted my comment.2011-08-27

1 Answers 1

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Note that $2\cdot 16^x=2\cdot (2^4)^x=2\cdot2^{4x}=2^{4x+1}$ and $4^{2x-2}=(2^2)^{2x-2}=2^{4x-4}.$ So you want to solve $2\cdot16^x-2^{4x}-4^{2x-2}=15$ $2^{4x+1}-2^{4x}-2^{4x-4}=15$ See any good ways of factoring something out on the left side of the equation? I think you might have reached this stage but made a minor calculation error. If you want to check your work, here is a spoiler (if you put your cursor over the box, the next step will appear):

$2^{4x-4}(2^5-2^4-1)=15$

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    Thank you for your help, finally solved it! =)2011-08-27