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Math Help - Simplify natural log expression

  1. #1
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    Simplify natural log expression

    Hi,

    I'm asked to simplify this expression:

    ln(\frac{x^2 - y^2}{\sqrt{x}})

    Using log rules, I did this:

    ln(x^2 - y^2) - ln(\sqrt{x})

    ln(x^2 - y^2) - \frac{1}{2}ln(x)

    Is it possible to simplify it further?
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  2. #2
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    Quote Originally Posted by centenial View Post
    Hi,

    I'm asked to simplify this expression:

    ln(\frac{x^2 - y^2}{\sqrt{x}})

    Using log rules, I did this:

    ln(x^2 - y^2) - ln(\sqrt{x})

    ln(x^2 - y^2) - \frac{1}{2}ln(x)

    Is it possible to simplify it further?
    No. There no simplification for log(a+ b) or log(a- b) so that cannot be simplified further.
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  3. #3
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    Thanks!
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  4. #4
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    Hello, centenial!

    I'm asked to simplify this expression:

    \ln\left(\frac{x^2 - y^2}{\sqrt{x}}\right)

    Using log rules, I did this:

    . . \ln(x^2 - y^2) - \ln(\sqrt{x})

    . . \ln(x^2 - y^2) - \tfrac{1}{2}\ln(x)

    Is it possible to simplify it further?

    HallsofIvy is correct!


    But if you want to show off, we can factor and separate the first log:

    . . \ln\bigg[(x-y)(x+y)\bigg] - \tfrac{1}{2}\ln(x) \;\;=\;\;\ln(x-y) + \ln(x+y) - \tfrac{1}{2}\ln(x)


    I suspect that this is the answer "they" expect.
    I asked myself, "Why did they use a factorable numerator?"

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