SOLUTION: Solve: 2^(x+1)*8^(-x) =4

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Question 149219: Solve: 2^(x+1)*8^(-x) =4
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
2%5E%28%28x%2B1%29%29+%2A+8%5E%28%28-x%29%29+=+4 Rewrite this as:
2%5E%28%28x%2B1%29%29%2F8%5Ex+=+4 Multiply both sides by 8%5Ex
2%5E%28%28x%2B1%29%29+=+4%2A8%5Ex Recall that:a%5En%2Aa%5Em+=+a%5E%28%28m%2Bn%29%29, so you can write:
2%5Ex%2A2%5E1+=+4%2A8%5Ex Divde both sides by 2 to simplify a bit.
2x+=+2%2A8%5Ex ,,,but 8%5Ex+=+%282%5E3%29%5Ex=2%5E%28%283x%29%29 Making this substitution, you get:
2%5Ex+=+2%2A2%5E%28%283x%29%29 = 2%5E%28%283x%2B1%29%29 Now, because the bases (2) are equal, the exponents are equal, so...
x+=+3x%2B1 Solve for x:
2x+=+-1
x+=+-%281%2F2%29
Let's check this solition:
2%5E%28%28x%2B1%29%29+%2A+8%5E%28-x%29+=+4 Substitute x+=+-%281%2F2%29
2%5E%28%28%28-1%2F2%29%2B1%29%29+%2A+8%5E%28%281%2F2%29%29+=+4 Simplify the left side.
2%5E%28%281%2F2%29%29+%2A+8%5E%28%281%2F2%29%29+=+4 Substitute8+=+2%5E3
2%5E%28%281%2F2%29%29+%2A+%282%5E3%29%5E%281%2F2%29+=+4 Simplify.
2%5E%28%281%2F2%29%29+%2A+2%5E%28%283%29%2F2%29+=+4 Simplify.
2%5E%281%2F2+%2B+3%2F2%29+=+4
2%5E%284%2F2%29+=+4
2%5E2+=+4
4+=+4