document.write( "Question 111220: I am having trouble solving equations with logs this is the problem i am stuck on...
\n" ); document.write( "log6(x+3)+log6(x+4)=1 \n" ); document.write( "

Algebra.Com's Answer #81130 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"log%286%2C%28x%2B3%29%29%2Blog%286%2C%28x%2B4%29%29+=+1\"$
\n" ); document.write( " $\"log%286%2C%28x%2B3%29%28x%2B4%29%29+=+1\"$
\n" ); document.write( "Written the other way,
\n" ); document.write( " $\"%28x%2B3%29%28x%2B4%29+=+6%5E1\"$
\n" ); document.write( " $\"x%5E2+%2B+7x+%2B+12+=+6\"$
\n" ); document.write( "subtract 12 from both sides and complete the square
\n" ); document.write( " $\"x%5E2+%2B+7x+%2B+%2849%2F4%29+=+-6+%2B+%2849%2F4%29\"$
\n" ); document.write( " $\"%28x+%2B+%287%2F2%29%29%5E2+=+%2849%2F4%29+-+%2824%2F4%29\"$
\n" ); document.write( " $\"%28x+%2B+%287%2F2%29%29%5E2+=+25%2F4\"$
\n" ); document.write( "take square root of both sides
\n" ); document.write( " $\"x+%2B+7%2F2+=+5%2F2\"$
\n" ); document.write( " $\"x+=+-1\"$ answer
\n" ); document.write( "Now plug into original equation to check
\n" ); document.write( " $\"log%286%2C%28x%2B3%29%29%2Blog%286%2C%28x%2B4%29%29+=+1\"$
\n" ); document.write( " $\"log%286%2C+-1+%2B+3%29+%2B+log%286%2C+-1+%2B+4%29+=+1\"$
\n" ); document.write( " $\"log%286%2C+2%29+%2B+log%286%2C+3%29+=+1\"$
\n" ); document.write( " $\"log%286%2C+2%2A3%29+=+1\"$
\n" ); document.write( " $\"log%286%2C+6%29+=+1\"$ checks OK
\n" ); document.write( "rewite it
\n" ); document.write( " $\"6%5E1+=+6\"$ true \n" ); document.write( "

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