document.write( "Question 252255: In the equation y=logbx, is it possible for x to have a negative value
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Algebra.Com's Answer #184080 by Edwin McCravy(20056)\"\" \"About 
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In the equation y=logbx, is it possible for x to have a negative value
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document.write( "Algebraically:\r\n" );
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document.write( "\"y=log%28b%2Cx%29\" means by definition \"b%5Ey=x\"\r\n" );
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document.write( "If y is positive, then \"x=b%5Ey\" is positive\r\n" );
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document.write( "If y is 0, then \"x=b%5Ey=b%5E0=1\" which is also positive\r\n" );
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document.write( "If y is negative, then \"x=b%5E%28-y%29+=+1%2F%28b%5Ey%29\" which is positive.\r\n" );
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document.write( "Therefore x can never be negative.\r\n" );
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document.write( "The graphs of \r\n" );
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document.write( "\"red%28y=log%282%2Cx%29%29\", \"green%28y=log%283%2Cx%29%29\", and \"blue%28y=log%285%2Cx%29%29\"\r\n" );
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document.write( "are plotted below\r\n" );
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document.write( "\"graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Clog%282%2Cx%29%2Clog%283%2Cx%29%2Clog%285%2Cx%29%29\" \r\n" );
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document.write( "And the graphs of \r\n" );
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document.write( "\"red%28y=log%281%2F2%2Cx%29%29\", \"green%28y=log%281%2F3%2Cx%29%29\", and \"blue%28y=log%281%2F5%2Cx%29%29\"\r\n" );
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document.write( "are plotted below\r\n" );
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document.write( "So you see there is never any graph in the 3rd or 4th quadrants\r\n" );
document.write( "where x is negative.\r\n" );
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document.write( "However in higher mathematics there are logarithms of negative\r\n" );
document.write( "numbers but they are imaginary numbers.  If you have a TI-84\r\n" );
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document.write( "PRESS MODE\r\n" );
document.write( "scroll down to REAL\r\n" );
document.write( "Press the right arrow key once\r\n" );
document.write( "Press ENTER\r\n" );
document.write( "Press 2nd\r\n" );
document.write( "Press MODE\r\n" );
document.write( "Press CLEAR\r\n" );
document.write( "Press LOG\r\n" );
document.write( "Press (-)\r\n" );
document.write( "Press 1\r\n" );
document.write( "Press )\r\n" );
document.write( "(Should see log(-1) on the screen\r\n" );
document.write( "Press ENTER\r\n" );
document.write( "Read 1.364376354i\r\n" );
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document.write( "See? It's imaginary.  It has an \"i\" on the end. \r\n" );
document.write( "You won't study that unless you take higher math \r\n" );
document.write( "in college.  You teacher may not even know that.\r\n" );
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document.write( "Edwin
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