document.write( "Question 416707: Please help me solve this equation! log2 x+ log2 (x+1)=1 \n" ); document.write( "
Algebra.Com's Answer #854216 by ikleyn(53750)\"\" \"About 
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\n" ); document.write( "Please help me solve this equation! log2 x+ log2 (x+1)=1
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\n" ); document.write( "\n" ); document.write( "        Below is my complete correct solution \r
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\n" ); document.write( "\n" ); document.write( "log2(x) + log2(x+1) = 1\r
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\n" ); document.write( "\n" ); document.write( "The domain for this equation is the set of all real positive numbers x > 0.\r
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\n" ); document.write( "\n" ); document.write( "In this domain, the given equation is equivalent to this one \r
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\n" ); document.write( "\n" ); document.write( "log2(x*(x+1)) = 1\r
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\n" ); document.write( "\n" ); document.write( "Simplify and find x\r
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\n" ); document.write( "\n" ); document.write( "x(x+1) = 2^1,
\n" ); document.write( "x^2+x-2 = 0
\n" ); document.write( "(x+2)(x-1) = 0
\n" ); document.write( "x = -2, 1\r
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\n" ); document.write( "\n" ); document.write( "x = -2 is an extraneous solution out the domain, so we disregard x = -2
\n" ); document.write( "(since logarithm of the negative argument is not defined).\r
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\n" ); document.write( "\n" ); document.write( "Thus, x = 1 is the unique real solution to the original equation.         <<<---===   ANSWER\r
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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