document.write( "Question 382936: solve for x: log x + (log x + 21)=2 \n" ); document.write( "

Algebra.Com's Answer #271266 by Earlsdon(6294) $\"\"$ $\"About$

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Solve for x:
\n" ); document.write( " $\"Log%28x%29%2BLog%28x%2B21%29+=+2\"$ Apply the product rule:
\n" ); document.write( " $\"Log%28%28x%29%28x%2B21%29%29+=+2\"$ Simplify the argument.
\n" ); document.write( " $\"Log%28x%5E2%2B21x%29+=+2\"$ Rewrite this in exponential form.
\n" ); document.write( " $\"10%5E2+=+x%5E2%2B21x\"$ Rewrite as a quadratic equation in standard form.
\n" ); document.write( " $\"x%5E2%2B21x-100+=+0\"$ Factor.
\n" ); document.write( " $\"%28x-4%29%28x%2B25%29+=+0\"$ Apply the zero product rule.
\n" ); document.write( " $\"%28x-4%29+=+0\"$ or $\"x%2B25+=+0\"$ so...
\n" ); document.write( " $\"x+=+4\"$ or $\"x+=+-25\"$ Discard the negative solution as the log of a negative number is not real.
\n" ); document.write( " $\"x+=+4\"$
\n" ); document.write( "Check:
\n" ); document.write( " $\"Log%284%29%2BLog%284%2B21%29+=+Log%284%29%2BLog%2825%29\"$ = $\"2\"$ \n" ); document.write( "

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