document.write( "Question 416851: log base 2 (x-2)+log base 2(8-x)-log base 2(x-5)=3 \n" ); document.write( "

Algebra.Com's Answer #853637 by MathTherapy(10699) $\"\"$ $\"About$

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document.write( "log base 2 (x-2)+log base 2(8-x)-log base 2(x-5)=3\r\n" );
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document.write( " Looking at the above, we see that x - 5 is SMALLER than x - 2, so we'll have: x - 5 > 0, which means that x > 5. \r\n" );
document.write( " Also, 8 - x MUST be > 0, so - x > - 8, and x < , so x < 8. We now get: \r\n" );
document.write( ", with 5 < x < 8 \r\n" );
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document.write( "                 (x - 2)(8 - x) = 8(x - 5)\r\n" );
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document.write( "                    <=== As seen HERE, the quadratic equation is NOT x^2 - 18x - 24 = 0, as @Stanbon states. \r\n" );
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document.write( "          - x(x - 6) - 4(x - 6) = 0\r\n" );
document.write( "               (x - 6)(- x - 4) = 0\r\n" );
document.write( "                x - 6 = 0       OR    - x - 4 = 0\r\n" );
document.write( "                   x = 6       OR    - 4 = x (IGNORE)\r\n" );
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document.write( "Of the 2 solutions above, ONLY the value 6, for x, is > 5, but < 8. This is why x = 6 is ACCEPTED as a solution, while x = - 4\r\n" );
document.write( "is IGNORED/REJECTED!!

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