document.write( "Question 1082312: Log 2 (x-2) + log 2 (x+1) =2 \n" ); document.write( "
Algebra.Com's Answer #696406 by ikleyn(52909)\"\" \"About 
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document.write( "\"log%282%2C%28x-2%29%29\" + \"log%282%2C%28x%2B1%29%29\" = 2 ---->\r\n" );
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document.write( "\"log%282%2C+%28%28x-2%29%2A%28x%2B1%29%29%29\" = 2                 (due to the property of logarithms \"log%28a%2C%28b%29%29\" + \"log%28a%2C%28c%29%29\" = \"log%28a%2C%28b%2Ac%29%29\" valid  for any base a>0 and any b>0, c>0)\r\n" );
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document.write( "\"log%282%2C%28x%5E2-x-2%29%29\" = 2  ---->\r\n" );
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document.write( "\"x%5E2+-+x+-+2\" = \"2%5E2\" = 4  ---->\r\n" );
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document.write( "\"x%5E2+-+x+-+6\" = 0  ---->\r\n" );
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document.write( "Factor left side:\r\n" );
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document.write( "(x+2)*(x-3) = 0.\r\n" );
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document.write( "The roots are x= -2 and x= 3.\r\n" );
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document.write( "Only the root x= 3 survives under logarithms.\r\n" );
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document.write( "Answer.  The only solution is x= 3.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On logarithms, their properties and logarithmic equations see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - WHAT IS the logarithm \r
\n" ); document.write( "\n" ); document.write( "    - Properties of the logarithm \r
\n" ); document.write( "\n" ); document.write( "    - Change of Base Formula for logarithms \r
\n" ); document.write( "\n" ); document.write( "    - Solving logarithmic equations \r
\n" ); document.write( "\n" ); document.write( "    - Using logarithms to solve real world problems \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Logarithms\".\r
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