document.write( "Question 246565: Hi,
\n" ); document.write( "I am stuck \r
\n" ); document.write( "\n" ); document.write( "log (x+6)-log(x+2)=log(x)\r
\n" ); document.write( "\n" ); document.write( "Does log(x) become 1, because 10^0?\r
\n" ); document.write( "\n" ); document.write( "Thank you in advance\r
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Algebra.Com's Answer #180013 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"log+%28%28x%2B6%29%29-log%28%28x%2B2%29%29=log%28%28x%29%29\"\r\n" );
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document.write( "Use the rule \"log%28%28A%29%29-log%28%28B%29%29=log%28%28A%2FB%29%29\" on the left side:\r\n" );
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document.write( "\"log%28%28%28x%2B6%29%2F%28x%2B2%29%29%29=log%28%28x%29%29\"\r\n" );
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document.write( "What the log is taken of on the left side must equal to\r\n" );
document.write( "what the log is taken of on the right side.\r\n" );
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document.write( "\"%28%28x%2B6%29%29%2F%28%28x%2B2%29%29=x\"\r\n" );
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document.write( "Multiply both sides by \"%28x%2B2%29\"\r\n" );
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document.write( "\"%28%28x%2B6%29%2F%28x%2B2%29%29%28x%2B2%29=x%28x%2B2%29\"\r\n" );
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document.write( "\"%28%28x%2B6%29%2F%28cross%28x%2B2%29%29%29%28cross%28x%2B2%29%29=x%28x%2B2%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"x%2B6=x%5E2%2B2x\"\r\n" );
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document.write( "\"0=x%5E2%2Bx-6\"\r\n" );
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document.write( "\"x%5E2%2Bx-6=0\"\r\n" );
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document.write( "\"%28x%2B3%29%28x-2%29=0\"\r\n" );
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document.write( "\"x%2B3=0\"       \"x-2=0\"\r\n" );
document.write( "\"x=-3\"         \"x=2\"\r\n" );
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document.write( "The negative solution must be discarded\r\n" );
document.write( "because it cannot be substituted in the \r\n" );
document.write( "term on the right of the original equation,\r\n" );
document.write( "\"log%28%28x%29%29\" for the log of a negative\r\n" );
document.write( "number is not a real number.\r\n" );
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document.write( "Therefore the only solution is \"x=2\"\r\n" );
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document.write( "Edwin
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