document.write( "Question 64539: Solve for x:\r
\n" ); document.write( "\n" ); document.write( "ln(x+1)-ln(x-2)=lnx \n" ); document.write( "
Algebra.Com's Answer #45157 by stanbon(75887)\"\" \"About 
You can put this solution on YOUR website!
ln(x+1)-ln(x-2)=lnx
\n" ); document.write( "Since lna - lnb = ln(a/b)
\n" ); document.write( "=ln[(x+1)/(x-2)]=lnx
\n" ); document.write( "If these ln's are equal the arguments must be equal:
\n" ); document.write( "(x+1)/(x-2)=x
\n" ); document.write( "Cross-multiply to get:
\n" ); document.write( "x+1=x^2-2x
\n" ); document.write( "x^2-3x-1=0
\n" ); document.write( "Using the quadratic formula you get:
\n" ); document.write( "x=[3+-sqrt(9-4(-1)]/2
\n" ); document.write( "x=[3+-sqrt13]/2
\n" ); document.write( "x=(3/2)1+(1/2)sqrt13 is the only solution as the alternate x=(3/2)-(1/2)sqrt13 is negative and cannot satisfy the original equation because
\n" ); document.write( "the original equation has a term lnx and ln(a negative number) is
\n" ); document.write( "not a defined number.
\n" ); document.write( "Let me know if this helps.
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \r
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