document.write( "Question 537901: Solve the equation.
\n" ); document.write( "2 log2(x) − log2(x - 3) = 2 + log2(4) \n" ); document.write( "

Algebra.Com's Answer #353034 by Earlsdon(6294) $\"\"$ $\"About$

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Solve for x:
\n" ); document.write( " $\"2Log%5B2%5D%28x%29-Log%5B2%5D%28x-3%29+=+2%2BLog%5B2%5D%284%29\"$ Apply the \"power rule\" to the first term on the left side.
\n" ); document.write( " $\"Log%5B2%5D%28x%5E2%29-Log%5B2%5D%28x-3%29+=+2%2BLog%5B2%5D%284%29\"$ Apply the \"quotient rule\" to the left side.
\n" ); document.write( " $\"Log%5B2%5D%28x%5E2%2F%28x-3%29%29+=+2%2BLog%5B2%5D%284%29\"$ Substitute $\"Log%5B2%5D%284%29+=+2\"$
\n" ); document.write( " $\"Log%5B2%5D%28x%5E2%2F%28x-3%29%29+=+2%2B2\"$
\n" ); document.write( " $\"Log%5B2%5D%28x%5E2%2F%28x-3%29%29+=+4\"$ Rewrite this in exponential form:
\n" ); document.write( " $\"2%5E4+=+x%5E2%2F%28x-3%29\"$ Substitute $\"2%5E4+=+16\"$
\n" ); document.write( " $\"16+=+x%5E2%2F%28x-3%29\"$ Multiply both sides by $\"%28x-3%29\"$
\n" ); document.write( " $\"16%28x-3%29+=+x%5E2\"$ Simplify.
\n" ); document.write( " $\"16x-48+=+x%5E2\"$ Rewrite as:
\n" ); document.write( " $\"x%5E2-16x%2B48+=+0\"$ Solve by factoring.
\n" ); document.write( " $\"%28x-4%29%28x-12%29+=+0\"$ Apply the \"zero product rule\".
\n" ); document.write( " $\"x-4+=+0\"$ or $\"x-12+=+0\"$ therefore:
\n" ); document.write( " $\"highlight%28x+=+4%29\"$ or $\"highlight_green%28x+=+12%29\"$ \n" ); document.write( "

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