SOLUTION: if 4^x+1 =2^x-1 find x

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Question 1055690: if 4^x+1 =2^x-1 find x
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
if 4^x+1 =2^x-1 find x
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4%5Ex%2B1+=2%5Ex-1
4%5Ex+-+2%5Ex+=+-2
2%5E%282x%29+-+2%5Ex+%2B+2+=+0
Sub u for 2^x
u%5E2+-+u+%2B+2+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1x%2B2+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-1%29%5E2-4%2A1%2A2=-7.

The discriminant -7 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -7 is + or - sqrt%28+7%29+=+2.64575131106459.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B2+%29

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No real number solutions.