SOLUTION: 2^x+4^x+8=28 Solve for X.

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Question 642134: 2^x+4^x+8=28
Solve for X.
Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

2^x+4^x+8=28
Solve for X.

2%5Ex+%2B+4%5Ex+%2B+8+=+28

2%5Ex+%2B+%282%5E2%29%5Ex+%2B+8+=+28

2%5Ex+%2B+2%5E%282x%29+%2B+8+-+28+=+0

2%5E%282x%29+%2B+2%5Ex+-+20+=+0 ---- Rearranging terms

2%5E%282x%29+%2B+1%282%5Ex%29+-+20+=+0

2%5E%282x%29+%2B+5%282%5Ex%29+-+4%282%5Ex%29+-+20+=+0

2%5Ex+%2A+%282%5Ex+%2B+5%29+-+4%282%5Ex+%2B+5%29+=+0

%282%5Ex+-+4%29%282%5Ex+%2B+5%29+=+0

2%5Ex+-+4+=+0 OR 2%5Ex+%2B+5+=+0

2%5Ex+=+4 OR 2%5Ex+=+-+5

2%5Ex+=+2%5E2 OR 2%5Ex+=+-+5 (IMPOSSIBLE, as no value raised to a power results in a negative value, so ignore)

highlight_green%28x+=+2%29

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Check
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2%5Ex+%2B+4%5Ex+%2B+8+=+28
2%5E2+%2B+4%5E2+%2B+8+=+28
4 + 16 + 8 = 28
28 = 28 (TRUE)

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