document.write( "Question 193260This question is from textbook Basic Technical Mathematics
\n" ); document.write( ": Hi Tutor,
\n" ); document.write( "I am stuck on this problem. ln(x+2)-ln(4)=-ln x
\n" ); document.write( "Do I take the ln of 2 and subtract the ln of 4? I don't know what else to do to solve thi1s.
\n" ); document.write( "Thank you
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Algebra.Com's Answer #145076 by nerdybill(7384)\"\" \"About 
You can put this solution on YOUR website!
Apply log rules:
\n" ); document.write( "ln(x+2)-ln(4)=-ln x
\n" ); document.write( "ln(x+2)-ln(4)+ln x = 0
\n" ); document.write( "ln[(x+2)/(4)]+ln x = 0
\n" ); document.write( "ln[x(x+2)/(4)] = 0
\n" ); document.write( "x(x+2)/(4) = e^0
\n" ); document.write( "x(x+2)/(4) = 1
\n" ); document.write( "x(x+2) = 4
\n" ); document.write( "x^2 + 2x = 4
\n" ); document.write( "x^2 + 2x - 4 = 0
\n" ); document.write( "Solve using the quadratic equation. Doing so yields:
\n" ); document.write( "x = {1.236, -3.236}
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\n" ); document.write( "We can throw out the negative solution, leaving:
\n" ); document.write( "x = 1.236
\n" ); document.write( ".
\n" ); document.write( "Details of quadratic to follow:
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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%2B2x%2B-4+=+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=%282%29%5E2-4%2A1%2A-4=20\".
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\n" ); document.write( " Discriminant d=20 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28-2%2B-sqrt%28+20+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%282%29%2Bsqrt%28+20+%29%29%2F2%5C1+=+1.23606797749979\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%282%29-sqrt%28+20+%29%29%2F2%5C1+=+-3.23606797749979\"
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\n" ); document.write( " Quadratic expression \"1x%5E2%2B2x%2B-4\" can be factored:
\n" ); document.write( " \"1x%5E2%2B2x%2B-4+=+1%28x-1.23606797749979%29%2A%28x--3.23606797749979%29\"
\n" ); document.write( " Again, the answer is: 1.23606797749979, -3.23606797749979.\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%2B2%2Ax%2B-4+%29\"

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