Question 1032298
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Find all real solutions x to 4^x - 2^x = 56.

Thank you!
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<U>Answer</U>. x = 3.

<U>Solution</U>

The standard method of solving equations similar to this one, is to introduce the new variable  y = {{{2^x}}}.

Then your original equation becomes 

{{{y^2 - y - 56}}} = {{{0}}}.

Factor it:

(y-8)*(y+7) = 0.

Only positive root does fit, since y = {{{2^x}}}.
So, y = 8.

Thus you have  {{{2^x}}} = 8,  which implies x = 3.
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