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Math Help - Natural Logarithms

  1. #1
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    Natural Logarithms

    In my answer book, I noticed that one of the steps were this:

    How did the first step lead to the second step? Can someone help me explain how?
    Last edited by !!!; October 22nd 2008 at 05:04 PM.
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  2. #2
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    x\ln(2x+1) + \frac{1}{2}\ln(2x+1) =

    factor out \ln(2x+1) ...

    \ln(2x+1) \cdot \left(x + \frac{1}{2}\right) =

    change the appearance of \left(x + \frac{1}{2}\right)

    \ln(2x+1) \cdot \frac{1}{2}(2x+1)
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  3. #3
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    change the appearance of \left(x + \frac{1}{2}\right)

    \ln(2x+1) \cdot \frac{1}{2}(2x+1)
    Thanks for responding, but what do you mean by "change the appearance"?
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  4. #4
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    \left(x+\frac{1}{2}\right) = \frac{1}{2}(2x+1)
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  5. #5
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    Quote Originally Posted by skeeter View Post
    \left(x+\frac{1}{2}\right) = \frac{1}{2}(2x+1)
    But how did that first part turn into the second part?
    EDIT: Nevermind, I got it now, thank you!
    Last edited by !!!; October 22nd 2008 at 06:03 PM.
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  6. #6
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    He just used logic to rewrite it in terms of the other polynomial.

    Distribute that out.

    \frac{1}{2} * 2x = x

    and

    \frac{1}{2} * 1 = \frac{1}{2}

    so

    \frac{1}{2}(2x + 1) = (x + \frac{1}{2})
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