document.write( "Question 427145: ln x + ln (x-2) = 1 \n" ); document.write( "
Algebra.Com's Answer #297052 by nerdybill(7384)\"\" \"About 
You can put this solution on YOUR website!
Applying log rules:
\n" ); document.write( "ln x + ln (x-2) = 1
\n" ); document.write( "ln x(x-2) = 1
\n" ); document.write( "x(x-2) = e^1
\n" ); document.write( "x^2-2x = e^1
\n" ); document.write( "x^2-2x - e^1 = 0
\n" ); document.write( "x^2-2x - 2.718 = 0
\n" ); document.write( "applying the quadratic formula we get:
\n" ); document.write( "x = {2.928, -0.928}
\n" ); document.write( "you can throw out the negative solution leaving:
\n" ); document.write( "x = 2.928
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\n" ); document.write( "details of quadratic follows:
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"1x%5E2%2B-2x%2B-2.718+=+0\") has the following solutons:
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\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
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\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%28-2%29%5E2-4%2A1%2A-2.718=14.872\".
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\n" ); document.write( " Discriminant d=14.872 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--2%2B-sqrt%28+14.872+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+14.872+%29%29%2F2%5C1+=+2.92821160664487\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-2%29-sqrt%28+14.872+%29%29%2F2%5C1+=+-0.928211606644872\"
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\n" ); document.write( " Quadratic expression \"1x%5E2%2B-2x%2B-2.718\" can be factored:
\n" ); document.write( " \"1x%5E2%2B-2x%2B-2.718+=+1%28x-2.92821160664487%29%2A%28x--0.928211606644872%29\"
\n" ); document.write( " Again, the answer is: 2.92821160664487, -0.928211606644872.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-2.718+%29\"

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