document.write( "Question 1206970: Solve algebraically: log2(2-2x) + log2(1-x)=5\r
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\n" ); document.write( "\n" ); document.write( "Solve algebraically: 2log(3-x)= log4 + log(6-x)\r
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Algebra.Com's Answer #844715 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "Solve algebraically: log2(2-2x) + log2(1-x)=5
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document.write( "Due to properties of logarithms, this equation is equivalent to \r\n" );
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document.write( "    (2-2x)*(1-x) =   in the domain  1-x > 0.\r\n" );
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document.write( "Simplify the last equation\r\n" );
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document.write( "    2 - 2x - 2x + 2x^2 = 32,   \r\n" );
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document.write( "    2x^2 - 4x - 30 = 0,\r\n" );
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document.write( "    x^2 - 2x - 15 = 0\r\n" );
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document.write( "    (x-5)*(x+3) = 0.\r\n" );
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document.write( "The solutions to the last equation are x= 5 and x= -3;  but only x= -3 is in the domain.\r\n" );
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document.write( "ANSWER.  The only solution is x = -3.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solve algebraically: 2log(3-x)= log4 + log(6-x)
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document.write( "Due to properties of logarithms, this equation is equivalent to\r\n" );
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document.write( "    (3-x)^2 = 4*(6-x)  in the domain  x < 3.\r\n" );
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document.write( "Simplfy the equation\r\n" );
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document.write( "    9 - 6x + x^2 = 24 - 4x\r\n" );
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document.write( "    x^2 -2x - 15 = 0\r\n" );
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document.write( "    (x-5)*(x+3) = 0.\r\n" );
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document.write( "The solutions to the last equation are x= 5 and x= -3;  but only x= -3 is in the domain.\r\n" );
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document.write( "ANSWER.  The only solution is x = -3.\r\n" );
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