document.write( "Question 143215: ln(x-1)-ln(x+1)=ln(x+5) \n" ); document.write( "
Algebra.Com's Answer #104210 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"+ln%28x-1%29-ln%28x%2B1%29=ln%28x%2B5%29\"\r\n" );
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document.write( "Use this principle of logarithms:  \"ln%28A%29-ln%28B%29=ln%28A%2FB%29\"\r\n" );
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document.write( "to rewrite the left side;\r\n" );
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document.write( "\"ln%28%28x-1%29%2F%28x%2B1%29%29=ln%28x%2B5%29\"\r\n" );
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document.write( "Now use the principle that \"ln%28A%29=ln%28B%29\" can be written as \"A=B\"\r\n" );
document.write( "to rewrite the whole equation:\r\n" );
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document.write( "\"%28x-1%29%2F%28x%2B1%29=x%2B5\"\r\n" );
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document.write( "Do you know how to solve that?  If not post again asking how.\r\n" );
document.write( "You get\r\n" );
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document.write( "x=-3, x = -2\r\n" );
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document.write( "But these must check in the original problem.\r\n" );
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document.write( "\"+ln%28x-1%29-ln%28x%2B1%29=ln%28x%2B5%29\"\r\n" );
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document.write( "Substitute x=-3 in the original\r\n" );
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document.write( "\"+ln%28-3-1%29-ln%28-3%2B1%29=ln%28-3%2B5%29\"\r\n" );
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document.write( "\"+ln%28-4%29-ln%28-2%29=ln%282%29\"\r\n" );
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document.write( "But there can be no logarithm of a negative number\r\n" );
document.write( "(except in advanced mathematics, but never in ordinary algebra).\r\n" );
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document.write( "So -3 is NOT a solution\r\n" );
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document.write( "Substitute x=-2 in the original\r\n" );
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document.write( "\"+ln%28-2-1%29-ln%28-2%2B1%29=ln%28-2%2B5%29\"\r\n" );
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document.write( "\"+ln%28-3%29-ln%28-1%29=ln%283%29\"\r\n" );
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document.write( "But, again, there can be no logarithm of a negative number\r\n" );
document.write( "in ordinary algebra.\r\n" );
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document.write( "Therefore -2 is not a solution either.\r\n" );
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document.write( "Therefore there is no solution to the equation.\r\n" );
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document.write( "Edwin
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