SOLUTION: ln(x-3)+lnx=10

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Question 667180: ln(x-3)+lnx=10
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
this is the "natural", or base-e log,
When e%5Ey=x, then base e logarithm of x is:
ln%28x%29=log_e%28x%29=y
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your solution:
ln%28x-3%29%2Blnx=10
ln%28%28x-3%29x%29=10
e%5Ey=x.....if y=10 we can write
%28%28x-3%29x%29=e%5E10
x%5E2-3x=e%5E10
x%5E2-3x-e%5E10=0...use quadratic formula to solve for x
x+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2Ae%5E10+%29%29%2F%282%2A1%29+
x+=+%283+%2B-+sqrt%28+9-4e%5E10+%29%29%2F2+
x=%281%2F2%29+%283%2Bsqrt%289%2B4+e%5E10%29%29