document.write( "Question 1208397: Solve for x\r
\n" ); document.write( "\n" ); document.write( "log(base 25)(x+1) + log(base 25)(x-3) = 1/2 \n" ); document.write( "
Algebra.Com's Answer #846794 by ikleyn(52781)\"\" \"About 
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\n" ); document.write( "log(base 25)(x+1) + log(base 25)(x-3) = 1/2
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document.write( "    \"log%2825%2C%28x%2B1%29%29\" + \"log%2825%2C%28x-3%29%29\" = \"1%2F2\"\r\n" );
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document.write( "    \"log%2825%2C%28%28x%2B1%29%2A%28x-3%29%29%29\" = \"1%2F2\"\r\n" );
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document.write( "Use the fact that  \"log%2825%2C5%29\" = \"1%2F2\"  and replace  \"1%2F2\"  in the right side \r\n" );
document.write( "of the previous equation by  \"log%2825%2C5%29\" = \"1%2F2\".  You will get\r\n" );
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document.write( "    \"log%2825%2C%28%28x%2B1%29%2A%28x-3%29%29%29\" = \"log%2825%2C5%29\".\r\n" );
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document.write( "It implies\r\n" );
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document.write( "    (x+1)*(x-3) = 5\r\n" );
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document.write( "    x^2 + x - 3x - 3 = 5\r\n" );
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document.write( "    x^2 - 2x - 8 = 0\r\n" );
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document.write( "    (x^2 - 2x + 1) - 8 = 1\r\n" );
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document.write( "     x^2 - 2x + 1 = 1 + 8\r\n" );
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document.write( "      (x-1)^2 = 9\r\n" );
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document.write( "       x-1    = +/- \"sqrt%289%29\" = +/- 3.\r\n" );
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document.write( "Hence, x is either -2 or 4.\r\n" );
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document.write( "Negative value x= -2 does not work in the original equation.\r\n" );
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document.write( "Hence,  x= 4  is the only solution.\r\n" );
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document.write( "ANSWER.  The only solution is x= 4.\r\n" );
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