SOLUTION: ln((2x+3)/(x^2-3x+2))^2 Write expression as the difference of logarithms. Express powers as factors.

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Question 549353: ln((2x+3)/(x^2-3x+2))^2
Write expression as the difference of logarithms. Express powers as factors.
Found 2 solutions by mathie123, Theo:
Answer by mathie123(224) About Me  (Show Source):
You can put this solution on YOUR website!
ln%28%282x%2B3%29%2F%28x%5E2-3x%2B2%29%29%5E2
Using the rule %28a%2Fb%29%5Ex=%28a%5Ex%29%2F%28b%5Ex%29 we can write our equation as
ln%28%28%282x%2B3%29%5E2%29%2F%28%28x%5E2-3x%2B2%29%5E2%29%29
Now using the rule ln%28a%2Fb%29=ln%28a%29-ln%28b%29 we can write our equation as
ln%28%282x%2B3%29%5E2%29-ln%28%28x%5E2-3x%2B2%29%5E2%29
And finally using the rule ln%28a%5Ex%29=x%2Aln%28a%29 we can write our equation as
2%2Aln%282x%2B3%29-2%2Aln%28x%5E2-3x%2B2%29
We could also factor out our common factor of 2 if we would like and get:
2%2A%28ln%282x%2B3%29-ln%28x%5E2-3x%2B2%29%29

Hopefully this helps!:)
Bre

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your answer, to the best of my determination, is shown in the following document.
$$$$$
your solution is in step number 5.
steps a, b, and c show the concepts used based on the properties of logarithms.
step number 1 shows the original problem as i understood it.
step number 2 applies concept a.
step number 3 applies concept b.
step number 4 factors x^2 - 3x + 2
step number 5 applies concept c.
i checked the original expression and the final expression in my calculator.
since the answers i got using both the original expression and the final expression matched, i assumed that the problem was solved correctly.
let me know if this is not what you were looking for.