document.write( "Question 1139555: log2(x)+log2(x-3)=2 \n" ); document.write( "

Algebra.Com's Answer #760038 by greenestamps(13203) $\"\"$ $\"About$

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\n" ); document.write( " $\"log%282%2C%28x%29%29%2Blog%282%2C%28x-3%29%29+=+2\"$

\n" ); document.write( "Rewrite the right side in terms of log base 2:

\n" ); document.write( " $\"log%282%2C%28x%29%29%2Blog%282%2C%28x-3%29%29+=+log%282%2C4%29\"$

\n" ); document.write( "Write the left side as a single logarithm using basic rules of logarithms:

\n" ); document.write( " $\"log%282%2C%28x%28x-3%29%29%29+=+log%282%2C4%29\"$

\n" ); document.write( "The logs are equal, so the arguments are equal:

\n" ); document.write( " $\"x%28x-3%29+=+4\"$
\n" ); document.write( " $\"x%5E2-3x-4+=+0\"$
\n" ); document.write( " $\"%28x-4%29%28x%2B1%29+=+0\"$

\n" ); document.write( " $\"x+=+4\"$ or $\"x+=+-1\"$

\n" ); document.write( "x=-1 does not work; the argument of a logarithm can't be negative.

\n" ); document.write( "x=4 works:

\n" ); document.write( " $\"log%282%2C4%29%2Blog%282%2C%284-3%29%29+=+log%282%2C4%29%2Blog%282%2C1%29+=+2%2B0+=+2\"$

\n" ); document.write( "ANSWER: x = 4 \n" ); document.write( "

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