document.write( "Question 78142: Please help me solve this equation. $\"lnx+%2B+ln%28x%2B1%29=2\"$ . I tried bringing the foil method bringing $\"%28x%2B1%29\"$ with $\"lnx\"$ , but all I ended up with was $\"ln+x%5E3=2\"$ and my teacher said that my steps were wrong. Can you help me to find out where it is exactly I went wrong. \n" ); document.write( "

Algebra.Com's Answer #56035 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
You cannot foil these parenthesis, you must use logarithmic identities to solve\r
\n" ); document.write( "\n" ); document.write( " $\"lnx+%2B+ln%28x%2B1%29=2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"ln%28x%2A%28x%2B1%29%29=2\"$ Use the identity: $\"ln%28x%29%2Bln%28y%29=ln%28x%2Ay%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"ln%28x%5E2%2Bx%29=2\"$ Distribute\r
\n" ); document.write( "\n" ); document.write( " $\"e%5E%28ln%28x%5E2%2Bx%29%29=e%5E2\"$ Raise both sides to exponents with the base of e. This undoes the natural log\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2Bx=e%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2Bx=e%5E2\"$ Subtract $\"e%5E2\"$ from both sides\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2Bx-e%5E2=0\"$ Since e^2 is approximately 7.3891 we can say\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2Bx-7.3891=0\"$ \r
\n" ); document.write( "\n" ); document.write( "Now use the quadratic formula:\r
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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"1x%5E2%2B1x%2B-7.3891+=+0\"$ ) 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 $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%281%29%5E2-4%2A1%2A-7.3891=30.5564\"$ .
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\n" ); document.write( " Discriminant d=30.5564 is greater than zero. That means that there are two solutions: $\"+x%5B12%5D+=+%28-1%2B-sqrt%28+30.5564+%29%29%2F2%5Ca\"$ .
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\n" ); document.write( " $\"x%5B1%5D+=+%28-%281%29%2Bsqrt%28+30.5564+%29%29%2F2%5C1+=+2.26389218313595\"$
\n" ); document.write( " $\"x%5B2%5D+=+%28-%281%29-sqrt%28+30.5564+%29%29%2F2%5C1+=+-3.26389218313595\"$
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\n" ); document.write( " Quadratic expression $\"1x%5E2%2B1x%2B-7.3891\"$ can be factored:
\n" ); document.write( " $\"1x%5E2%2B1x%2B-7.3891+=+1%28x-2.26389218313595%29%2A%28x--3.26389218313595%29\"$
\n" ); document.write( " Again, the answer is: 2.26389218313595, -3.26389218313595.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-7.3891+%29\"$

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\n" ); document.write( "\n" ); document.write( "So our answer is \r
\n" ); document.write( "\n" ); document.write( " $\"x=-3.26389218313595\"$ or $\"x=2.26389218313595\"$ \n" ); document.write( "

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