document.write( "Question 80095: Solve the logarithmic equation log x + log (x-3)= 1 \n" ); document.write( "
Algebra.Com's Answer #57452 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "log(x) + log (x-3) = 1\r\n" );
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document.write( "When you take a log out of two terms, an addition becomes \r\n" );
document.write( "a multiplication and a subtraction becomes a division:\r\n" );
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document.write( "     log[(x)(x-3)] = 1\r\n" );
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document.write( "Now take the antilog of both sides, remembering that the\r\n" );
document.write( "antilog of 1 is 10.\r\n" );
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document.write( "         (x)(x-3) = 10\r\n" );
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document.write( "     x² - 3x - 10 = 0\r\n" );
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document.write( "   (x - 5)(x + 2) = 0\r\n" );
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document.write( "Set the first factor = 0\r\n" );
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document.write( "            x - 5 = 0.\r\n" );
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document.write( "                x = 5\r\n" );
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document.write( "That checks:\r\n" );
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document.write( "           log(x) + log(x-3)= 1\r\n" );
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document.write( "          log(5) + log(5-3) = 1\r\n" );
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document.write( "            log(5) + log(2) = 1\r\n" );
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document.write( ".6989700043 + .301010299957 = 1\r\n" );
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document.write( "                          1 = 1 \r\n" );
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document.write( "Set the secod factor = 0\r\n" );
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document.write( " x + 2 = 0\r\n" );
document.write( "   x = -2   \r\n" );
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document.write( "We must discard that, because when\r\n" );
document.write( "we try to check it:\r\n" );
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document.write( "log(-2) + log(-2-3) = 1\r\n" );
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document.write( "log(-2) + log(-5) = 1\r\n" );
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document.write( "Logs can only be taken of positive\r\n" );
document.write( "numbers, so the left side is not defined.\r\n" );
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document.write( "There is but one solution, x = 5\r\n" );
document.write( "That involves log(0) which is not\r\n" );
document.write( "defined.\r\n" );
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document.write( "Edwin
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