document.write( "Question 39229This question is from textbook Algebra 2
\n" ); document.write( ": Ln(x)+Ln(x-2)=1 \n" ); document.write( "
Algebra.Com's Answer #24652 by Nate(3500)\"\" \"About 
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Ln(x)+Ln(x-2)=1
\n" ); document.write( "Ln((x)(x-2))=1
\n" ); document.write( "Ln(x^2-2x)=1
\n" ); document.write( "x^2-2x=e
\n" ); document.write( "x^2-2x-e=0
\n" ); document.write( "Looks a little like what is below. No solutions exist.
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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%2B2.718281828+=+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%2A2.718281828=-6.873127312\".
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\n" ); document.write( " The discriminant -6.873127312 is less than zero. That means that there are no solutions among real numbers.

\n" ); document.write( " If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

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\n" ); document.write( " In the field of imaginary numbers, the square root of -6.873127312 is + or - \"sqrt%28+6.873127312%29+=+2.62166498851398\".
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\n" ); document.write( " The solution is
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\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%2B2.718281828+%29\"
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