SOLUTION: ln(x+3)+ ln(x)=1

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Question 627462: ln(x+3)+ ln(x)=1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
ln%28x%2B3%29%2B+ln%28x%29=1

ln%28x%28x%2B3%29%29=1

x%28x%2B3%29=e%5E1

x%28x%2B3%29=e

x%28x%2B3%29+=+e

x%5E2+%2B+3x+=+e

x%5E2+%2B+3x+-+e+=+0

Now use the quadratic formula to solve for x

x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

x+=+%28-%283%29%2B-sqrt%28%283%29%5E2-4%281%29%28-e%29%29%29%2F%282%281%29%29

x+=+%28-3%2B-sqrt%289%2B4e%29%29%2F%282%29

x+=+%28-3%2Bsqrt%289%2B4e%29%29%2F%282%29 or x+=+%28-3-sqrt%289%2B4e%29%29%2F%282%29

So the possible solutions are x+=+%28-3%2Bsqrt%289%2B4e%29%29%2F%282%29 or x+=+%0D%0A%28-3-sqrt%289%2B4e%29%29%2F%282%29

which approximate to x = 0.72896 or x = -3.72896

However, notice how the second possible solution is negative...which is not
allowed.

So we toss that solution.

Therefore, the only solution is approximately x = 0.72896