document.write( "Question 200476: \"+log+%28+3%2C+%28+x-+2%29+%29+%2B+log+%283%2C+%28+x-+4%29+%29+=+2+\" \n" ); document.write( "
Algebra.Com's Answer #150727 by nerdybill(7384)\"\" \"About 
You can put this solution on YOUR website!
Applying log rules:
\n" ); document.write( "\"+log+%28+3%2C+%28+x-+2%29+%29+%2B+log+%283%2C+%28+x-+4%29+%29+=+2+\"
\n" ); document.write( "\"+log+%28+3%2C+%28+x-+2%29%28+x-+4%29+%29+=+2+\"
\n" ); document.write( "\"+%28+x-+2%29%28+x-+4%29+=+3%5E2+\"
\n" ); document.write( "\"+x%5E2-+4x+-2x+%2B8+=+9+\"
\n" ); document.write( "\"+x%5E2-+6x+%2B8+=+9+\"
\n" ); document.write( "\"+x%5E2-+6x+-+1+=+0+\"
\n" ); document.write( "Solving for x using the quadratic equation yields:
\n" ); document.write( "x = {6.162, -0.162}
\n" ); document.write( "We can throw out the negative solution leaving:
\n" ); document.write( "x = 6.162
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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-6x%2B-1+=+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=%28-6%29%5E2-4%2A1%2A-1=40\".
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\n" ); document.write( " Discriminant d=40 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--6%2B-sqrt%28+40+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+40+%29%29%2F2%5C1+=+6.16227766016838\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-6%29-sqrt%28+40+%29%29%2F2%5C1+=+-0.16227766016838\"
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\n" ); document.write( " Quadratic expression \"1x%5E2%2B-6x%2B-1\" can be factored:
\n" ); document.write( " \"1x%5E2%2B-6x%2B-1+=+1%28x-6.16227766016838%29%2A%28x--0.16227766016838%29\"
\n" ); document.write( " Again, the answer is: 6.16227766016838, -0.16227766016838.\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-6%2Ax%2B-1+%29\"
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