document.write( "Question 468208: I need a little help here:\r
\n" ); document.write( "\n" ); document.write( "ln(x+9)-ln(x-5)=ln(x+7)-ln(x-4).\r
\n" ); document.write( "\n" ); document.write( "Apparently there is no solution? Why not x=1/3?! \n" ); document.write( "

Algebra.Com's Answer #321256 by stanbon(75887) $\"\"$ $\"About$

You can put this solution on YOUR website!
ln(x+9)-ln(x-5)=ln(x+7)-ln(x-4).
\n" ); document.write( "---
\n" ); document.write( "ln[(x+9)/(x-5)] = ln[(x+7)/(x-4)]
\n" ); document.write( "----
\n" ); document.write( "(x+9)/(x-5) = (x+7)/(x-4)
\n" ); document.write( "---
\n" ); document.write( "Cross-multiply
\n" ); document.write( "x^2 + 5x - 36 = x^2 + 2x - 35
\n" ); document.write( "----
\n" ); document.write( "3x = 1
\n" ); document.write( "x = 1/3
\n" ); document.write( "-----
\n" ); document.write( "Why is that not a solution?
\n" ); document.write( "If you substitute that into the original equation
\n" ); document.write( "you would get:
\n" ); document.write( "ln((1/3)+9) - ln((1/3)-5) = ln((1/3)+7 - ln((1/3)-4)]
\n" ); document.write( "---
\n" ); document.write( "The ln((1/3)-5) and the ln((1/3)-4) are both undefined.
\n" ); document.write( "because there is not ln of a negative number.
\n" ); document.write( "------
\n" ); document.write( "Therefore, no solution.
\n" ); document.write( "===========================
\n" ); document.write( "cheers,
\n" ); document.write( "stan H. \n" ); document.write( "

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