document.write( "Question 1061353: If f(x) = (x-3) logx, then prove the equation xlogx = 3-x is satisfied by at least one value of x lying between 1 and 3. \n" ); document.write( "

Algebra.Com's Answer #676150 by Edwin McCravy(20059) $\"\"$ $\"About$

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document.write( "This problem might as well be stated:\r\n" );
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document.write( "\"If the capital of Georgia is Atlanta, then prove the equation \r\n" );
document.write( "xlogx = 3-x is satisfied by at least one value of x lying \r\n" );
document.write( "between 1 and 3.\"\r\n" );
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document.write( "That's because \"f(x) = (x-3)logx\" has no more to do with whether\r\n" );
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document.write( "\"the equation xlogx = 3-x is satisfied by at least one value of x \r\n" );
document.write( "lying between 1 and 3\" than the capital of Georgia being Atlanta \r\n" );
document.write( "has to do with it!\r\n" );
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document.write( "Thus we ignore the f(x) part and take the problem to be:\r\n" );
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document.write( "Prove that the equation \r\n" );
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document.write( "is satisfied by at least one value of x lying between 1 and 3.\r\n" );
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document.write( "Consider the function which is continuous on [1,3]\r\n" );
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document.write( "g(1) is negative and g(3) is positive.\r\n" );
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document.write( "Thus there is some number, say h, on [1,3] such that\r\n" );
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document.write( "Thus\r\n" );
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document.write( "and\r\n" );
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document.write( "[Note: If you require that h be an algebraic number then\r\n" );
document.write( "choose h to be ]\r\n" );
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document.write( "Edwin

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