SOLUTION: Find all real solutions x to 4^x - 2^x = 56. Thank you!

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Question 1032298: Find all real solutions x to 4^x - 2^x = 56.
Thank you!
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
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Find all real solutions x to 4^x - 2^x = 56.
Thank you!
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Answer. x = 3.

Solution

The standard method of solving equations similar to this one, is to introduce the new variable  y = 2%5Ex.

Then your original equation becomes 

y%5E2+-+y+-+56 = 0.

Factor it:

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

Only positive root does fit, since y = 2%5Ex.
So, y = 8.

Thus you have  2%5Ex = 8,  which implies x = 3.