document.write( "Question 1094663: log(x+14)+log(x+2)=6
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Algebra.Com's Answer #709240 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"log%28%28x%2B14%29%29%2Blog%28%28x%2B2%29%29\"\"%22%22=%22%22\"\"6\"\r\n" );
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document.write( "Use the principle: \"log%28B%2C%28A%29%29%2Blog%28B%2C%28C%29%29=log%28B%2C%28A%2AC%29%29\" to write\r\n" );
document.write( "the left side as a single logarithm:\r\n" );
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document.write( "\"log%28%28%28x%2B14%29%5E%22%22%28x%2B2%29%29%29\"\"%22%22=%22%22\"\"6\"\r\n" );
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document.write( "Use the principle: \"log%28%28A%29%29=log%2810%2C%28A%29%29\" to put in the understood\r\n" );
document.write( "logarithm base:\r\n" );
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document.write( "\"log%2810%2C%28%28x%2B14%29%5E%22%22%28x%2B2%29%29%29\"\"%22%22=%22%22\"\"6\"\r\n" );
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document.write( "Use the principle that the logarithm equation \"log%28B%2C%28A%29%29=C\" is equivalent\r\n" );
document.write( "to the exponential equation \"A=B%5EC\" to rewrite the above logatithm\r\n" );
document.write( "equation as an exponential equation:\r\n" );
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document.write( "\"%28x%2B14%29%28x%2B2%29\"\"%22%22=%22%22\"\"10%5E6\"\r\n" );
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document.write( "\"x%5E2%2B16x%2B28%29\"\"%22%22=%22%22\"\"1000000\"\r\n" );
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document.write( "\"x%5E2%2B16x-999972%29\"\"%22%22=%22%22\"\"0\"\r\n" );
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document.write( "Substitute a=1, b=16, and c=-999972 in the quadratic formula:\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29+\"\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"%28-%2816%29+%2B-+sqrt%28%2816%29%5E2-4%281%29%28-999972%29%29%29%2F%282%281%29%29+\"\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"%28-16+%2B-+sqrt%28256%2B3999888%29%29%2F2+\"\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"%28-16+%2B-+sqrt%284000144%29%29%2F2+\"\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"%28-16+%2B-+sqrt%2816%2A250009%29%29%2F2+\"\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"%28-16+%2B-+4sqrt%28250009%29%29%2F2+\"\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"%28-16%29%2F2+%2B-+%284sqrt%28250009%29%29%2F2+\"\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"-8+%2B-+2sqrt%28250009%29+\"\r\n" );
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document.write( "We discard the negative answer since logarithms of negative\r\n" );
document.write( "numbers are not real.  So the only solution is\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"-8+%2B+2sqrt%28250009%29+\"\r\n" );
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document.write( "That's approximately 992.0179998\r\n" );
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document.write( "Edwin
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