document.write( "Question 469443: solve for x: log2x+ log(2x-1)=1 \n" ); document.write( "

Algebra.Com's Answer #322098 by Tatiana_Stebko(1539) $\"\"$ $\"About$

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$\"log%28%282x%29%29%2B+log%28%282x-1%29%29=1\"$
\n" ); document.write( " $\"system%282x%3E0%2C2x-1%3E0%29\"$ => $\"system%28x%3E0%2C2x%3E1%29\"$ => $\"system%28x%3E0%2Cx%3E1%2F2%29\"$ => $\"x%3E1%2F2\"$
\n" ); document.write( "Use formula $\"log%28c%2Ca%29%2Blog%28c%2Cb%29=log%28c%2C%28a%2Ab%29%29\"$
\n" ); document.write( " $\"log%282x%2A%282x-1%29%29+=1\"$
\n" ); document.write( "Use formula $\"log%28c%2Ca%29=b\"$ <=> $\"a=c%5Eb\"$
\n" ); document.write( " $\"2x%2A%282x-1%29+=10%5E1\"$
\n" ); document.write( " $\"2x%2A%282x-1%29+=10\"$ divide by 2
\n" ); document.write( " $\"x%282x-1%29=5\"$
\n" ); document.write( " $\"2x%5E2-x-5=0\"$
\n" ); document.write( " $\"x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A2%2A%28-5%29+%29%29%2F%282%2A2%29+\"$
\n" ); document.write( " $\"x+=+%281+%2B-+sqrt%28+41%29%29%2F4+\"$
\n" ); document.write( " $\"x+=+%281+-+sqrt%28+41%29%29%2F4+=-1.35%3C1%2F2\"$ extraneous root
\n" ); document.write( " $\"x+=+%281+%2B+sqrt%28+41%29%29%2F4=1.85+\"$ \r
\n" ); document.write( "
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