document.write( "Question 306865: I need help on a logarithm problem.\r
\n" ); document.write( "\n" ); document.write( "I need to Solve for X.\r
\n" ); document.write( "\n" ); document.write( "2ln(x)-ln(x+8/3)= ln(6) \n" ); document.write( "
Algebra.Com's Answer #219542 by nerdybill(7384)\"\" \"About 
You can put this solution on YOUR website!
2ln(x)-ln((x+8)/3)= ln(6)
\n" ); document.write( "ln(x^2)-ln((x+8)/3)= ln(6)
\n" ); document.write( "ln(x^2)/((x+8)/3)= ln(6)
\n" ); document.write( "(x^2)/((x+8)/3)= 6
\n" ); document.write( "(x^2) = 6((x+8)/3)
\n" ); document.write( "(x^2) = 2(x+8)
\n" ); document.write( "(x^2) = 2x+16
\n" ); document.write( "x^2-2x-16 = 0
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\n" ); document.write( "Solve by applying the quadratic formula. Doing so yields:
\n" ); document.write( "x = {5.123, -3.123}
\n" ); document.write( "Toss out the negative solution (extraneous) leaving:
\n" ); document.write( "x = 5.123
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\n" ); document.write( "Details of quadratic formula 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-16+=+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-16=68\".
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\n" ); document.write( " Discriminant d=68 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--2%2B-sqrt%28+68+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+68+%29%29%2F2%5C1+=+5.12310562561766\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-2%29-sqrt%28+68+%29%29%2F2%5C1+=+-3.12310562561766\"
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\n" ); document.write( " Quadratic expression \"1x%5E2%2B-2x%2B-16\" can be factored:
\n" ); document.write( " \"1x%5E2%2B-2x%2B-16+=+1%28x-5.12310562561766%29%2A%28x--3.12310562561766%29\"
\n" ); document.write( " Again, the answer is: 5.12310562561766, -3.12310562561766.\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-16+%29\"

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