document.write( "Question 741763: ln(−8 − x) + ln 3 = ln(2 − x) \n" ); document.write( "

Algebra.Com's Answer #852620 by ikleyn(53426) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Solve the equation
\n" ); document.write( "ln(−8 − x) + ln 3 = ln(2 − x)
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document.write( "The domain to this equation is the solution set to these two inequalities\r\n" );
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document.write( "    -8 - x > 0  AND  2 - x > 0.\r\n" );
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document.write( "They define the domain as the set  { x | x < -8 }.\r\n" );
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document.write( "So, we will assume that 'x' is in this domain.\r\n" );
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document.write( "Then from the given equation, due to the properties of logarithms, we have\r\n" );
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document.write( "    (-8 - x)*3 = 2 - x,\r\n" );
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document.write( "    -24 - 3x = 2 - x\r\n" );
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document.write( "     -24 - 2 = 3x - x\r\n" );
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document.write( "        -26  =   2x\r\n" );
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document.write( "        x = -26/2 = -13.\r\n" );
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document.write( "This value -13 is in the domain, so it is the solution to the given equation.   ANSWER\r\n" );
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document.write( "You may CHECK  that at x = -13  both sides of the given equation are ln(15): \r\n" );
document.write( "they coincide, so the answer  is correct.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "What is written in the post by @lynnlo is a blatant gibberish,
\n" ); document.write( "so ignore his/her post for the peace in your mind.\r
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