document.write( "Question 186597: Hi guys, im stumped with this one:\r
\n" ); document.write( "\n" ); document.write( "2ln2 - ln(x-1) = ln(2x)\r
\n" ); document.write( "\n" ); document.write( "solve for 'x'.\r
\n" ); document.write( "\n" ); document.write( "cheers =)
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Algebra.Com's Answer #139860 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
In general:
\n" ); document.write( "\"log%28a%29+-+log%28b%29+=+log%28a%2Fb%29\"
\n" ); document.write( "and
\n" ); document.write( "\"a%2Alog%28b%29+=+log%28a%5Eb%29\"
\n" ); document.write( "\"2ln%282%29+-+ln%28x-1%29+=+ln%282x%29\"
\n" ); document.write( "\"ln%282%5E2%29+-+ln%28x-1%29+=+ln%282x%29\"
\n" ); document.write( "\"ln%284%2F%28x-1%29%29+=+ln%282x%29\"
\n" ); document.write( "\"4%2F%28x-1%29+=+2x\"
\n" ); document.write( "\"4+=+2x%2A%28x-1%29\"
\n" ); document.write( "\"4+=+2x%5E2+-+2x\"
\n" ); document.write( "\"2x%5E2+-+2x+-+4+=+0\"
\n" ); document.write( "\"x%5E2+-+x+-+2+=+0\"
\n" ); document.write( "\"%28x+-+2%29%28x+%2B+1%29+=+0\"
\n" ); document.write( "\"x+=+2\"
\n" ); document.write( "\"x+=+-1\"
\n" ); document.write( "check:
\n" ); document.write( "\"2ln%282%29+-+ln%28x-1%29+=+ln%282x%29\"
\n" ); document.write( "\"2ln%282%29+-+ln%282-1%29+=+ln%282%2A2%29\"
\n" ); document.write( "\"ln%284%29+-+ln%281%29+=+ln%284%29\"
\n" ); document.write( "\"ln%284%29+-+0+=+ln%284%29\"
\n" ); document.write( "OK
\n" ); document.write( "\"2ln%282%29+-+ln%28x-1%29+=+ln%282x%29\"
\n" ); document.write( "\"2ln%282%29+-+ln%28-1-1%29+=+ln%282%2A%28-1%29%29\"
\n" ); document.write( "The negative root doesn't work since
\n" ); document.write( "raising \"e\" to a power can't
\n" ); document.write( "result in a negative
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