document.write( "Question 1153079: log(base 5)(x-2) + log (base 5)(x-6) =1. Find all of the values of x. \n" ); document.write( "

Algebra.Com's Answer #775235 by ikleyn(52817) $\"\"$ $\"About$

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document.write( "From the given equation,\r\n" );
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document.write( "    (x-2)*(x-6) = 5.    (1)\r\n" );
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document.write( "The numbers, whose product is 5 and that differ 4 units, are the pairs  (1,5) and (-1,-5).\r\n" );
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document.write( "So,  x-2 = 5,  x = 5 + 2 = 7  is one solution,  while\r\n" );
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document.write( "     x-2 = -1,  x = 1   is formally another solution to the quadratic equation (1).\r\n" );
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document.write( "But under the logarithm, only the solution x = 7 survives.\r\n" );
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document.write( "ANSWER.  x = 7 is the ONLY solution to the given logarithmic equation.\r\n" );
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