document.write( "Question 799168: Express as a single term  
\n" ); document.write( "1/7 ln(x + 2)^7 + 1/2[lnx − ln(x^2 + 3x + 2)^2]\r
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Algebra.Com's Answer #482534 by DrBeeee(684)\"\" \"About 
You can put this solution on YOUR website!
Given;
\n" ); document.write( "(1) 1/7ln(x+2)^7 + 1/2[ln(x) - ln(x^2+3x+2)^2]
\n" ); document.write( "Using the property
\n" ); document.write( "(2) a*ln(b)^c = ln(b)^a*c
\n" ); document.write( "and simplifying the second term yields
\n" ); document.write( "(3) ln(x+2)^(7/7) + 1/2ln(x) - 1/2ln(x^2+3x+2)^2 or
\n" ); document.write( "(4) ln(x+2) + 1/2ln(x) - 1/2ln(x^2+3x+2)^2
\n" ); document.write( "Now apply (2) to the second and third terms of (4) to yield
\n" ); document.write( "(5) ln(x+2) + ln(sqrt(x)) - ln(x^2+3x+2)^(2/2) or
\n" ); document.write( "(6) ln(x+2) + ln(sqrt(x)) - ln(x^2+3x+2)
\n" ); document.write( "Now factor the quadratic in the third term to get
\n" ); document.write( "(7) ln(x+2) + ln(sqrt(x)) - ln[(x+2)*(x+1)]
\n" ); document.write( "Now use the property
\n" ); document.write( "(8) ln(a*b) = ln(a) + ln(b)
\n" ); document.write( "in the third term of (7) to get
\n" ); document.write( "(9) ln(x+2) + ln(sqrt(x)) - ln(x^2) - ln(x+1)
\n" ); document.write( "Note that the first and third terms of (9) cancel, leaving
\n" ); document.write( "(10) ln(sqrt(x)) - ln(x+1)
\n" ); document.write( "Now use the property
\n" ); document.write( "(11) ln(a/b) = ln(a) - ln(b)
\n" ); document.write( "in (10) to yield the final answer
\n" ); document.write( "(12) \"ln%28sqrt%28x%29%2F%28x%2B1%29%29\"\r
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