document.write( "Question 166689: log3(x-2)+log3(x+4)=3 \n" ); document.write( "

Algebra.Com's Answer #853883 by MathTherapy(10801) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "log3(x-2)+log3(x+4)=3\r\n" );
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document.write( "The other person who responded is WRONG!! His solutions, \"x = {3.243, -5.243}\" are WRONG.\r\n" );
document.write( "If he'd checked his answers, he would've realized this.\r\n" );
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document.write( "The SMALLER log argument, x - 2 MUST be > 0, so x - 2 > 0, and we get: x > 2. We now have:\r\n" );
document.write( ", with x being > 2.\r\n" );
document.write( "         ----- Applying  = \r\n" );
document.write( "               ---- Converting to EXPONENTIAL form\r\n" );
document.write( "                 \r\n" );
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document.write( "               \r\n" );
document.write( "       (x - 5)(x + 7) = 0\r\n" );
document.write( "        x - 5 = 0        OR        x + 7 = 0\r\n" );
document.write( "              x = 5        OR               x = - 7 (ignore)\r\n" );
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document.write( "The constraint above \"states\" that x MUST be > 2. 5 is > 2, but - 7 is NOT. This makes - 7 an\r\n" );
document.write( "EXTRANEOUS solution, and the only ACCEPTABLE solution, x  = 5.\r\n" );
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document.write( "You can do the CHECK!!

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