SOLUTION: Solve for x: {{{7^(x+2)-7^x=48*sqrt( 7 )}}}

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Question 565424: Solve for x:
7%5E%28x%2B2%29-7%5Ex=48%2Asqrt%28+7+%29
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
7%5E%28x%2B2%29-7%5Ex=48%2Asqrt%28+7+%29
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We can factor the expression as follows:
7%5Ex%2A%287%5E2-1%29=48%2Asqrt%287%29
7%5Ex%2A%2848%29+=+48%2Asqrt%287%29
7%5Ex+=+sqrt%287%29+=+7%5E%281%2F2%29
From here, we can read off the answer x = 1/2, or solve using logarithms:
x%2Alog%287%29+=+%281%2F2%29%2Alog%287%29
Dividing through be log(7) gives x = 1/2