Algebra.Com's Answer #832329 by ikleyn(52800)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Aplique a propriedade do logaritmo \r
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document.write( "Log2 (4x2)
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document.write( " This problem, harmless at first sight, has a huge underwater stone, like a trap,\r
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document.write( " which was overlooked by other tutors.\r
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document.write( "We start from this expression  .\r\n" );
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document.write( "In this expression, x can be any non-zero number, negative or positive.\r\n" );
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document.write( "In other words, the domain, where the expression is defined / (makes sense), \r\n" );
document.write( "is the set of all real non-zero numbers {R \ {0} }.\r\n" );
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document.write( "In this domain\r\n" );
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document.write( " =  +  =  .\r\n" );
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document.write( "Now,  =  is valid for all values of x in the domain, positive or negative,\r\n" );
document.write( "excluding the zero value of x. Notice the absolute value sign under the logarithm.\r\n" );
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document.write( "Therefore, in the entire domain, =  .\r\n" );
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document.write( "It does not matter if you take the factor of \"2\" outside the parentheses or not.\r\n" );
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document.write( "What is REALLY IMPORTANT, is to use the sign of absolute value,  , under the logarithm \r\n" );
document.write( "in the final expression.\r\n" );
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document.write( "Then (and only then) the identity \r\n" );
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document.write( " = .\r\n" );
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document.write( "is valid on the entire domain, which is {R \ {0} }, the set of all real non-zero numbers.\r\n" );
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document.write( "Solved.\r
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document.write( "The meaning of this assignment is to simplify the given expression accurately over the entire domain.\r
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