document.write( "Question 895516: log4x-log4(x+3)=log4(x-2) \n" ); document.write( "
Algebra.Com's Answer #542862 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "log4x-log4(x+3) = log4(x-2)\r\n" );
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document.write( "Get all logs on the side of the equation where they will be positive\r\n" );
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document.write( "log4x = log4(x+3) + log4(x-2)\r\n" );
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document.write( "The left side is already a single log.  We get the right side\r\n" );
document.write( "to a single log also.  To do this we remember that the sum of logs\r\n" );
document.write( "is the log of the product:\r\n" );
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document.write( "log4x = log4[(x+3)(x-2)] \r\n" );
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document.write( "Now that we have single logs on both sides we can drop the logs\r\n" );
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document.write( "x = (x+3)(x-2)\r\n" );
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document.write( "x = x²+x-6\r\n" );
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document.write( "0 = x²-6\r\n" );
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document.write( "6 = x²\r\n" );
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document.write( "±√6 = x\r\n" );
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document.write( "But since we cannot take logs of negative numbers, we must discard\r\n" );
document.write( "the negative solution, sinc the original equation has term log4x.\r\n" );
document.write( "However √6 causes us to only have to take logs of positive solutions, \r\n" );
document.write( "so it is a solution.\r\n" );
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document.write( "Therefore the only solution is √6 \r\n" );
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document.write( "Edwin
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