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Math Help - logarithmic simplification.

  1. #1
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    logarithmic simplification.

    Express the given quantity as a single logarithm.



    and now for my attempt

    oh, BTW, sqrt = square root. I dont know how to make the symbol on this forum.

    ln(1+x^6)-ln(cos(x))+(ln(x)/2)

    ln((1+x^6)/(cos(x))+ln(x)/2

    ln((1+x^6)/(cos(x))+ln(sqrt(x))

    ln((1+x^6)/(cos(x)(ln(sqrt(x))

    ln((sqrt(x)(x^6+1))/cos(x))

    man, I wish I could make this look nicer so its easier to read. But anyway, that last entry is what I got. I just want to be sure.
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  2. #2
    Moo
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    Hello,

    Yup, that's correct !

    As for the codes :

    \frac{numerator}{denominator} gives \frac{numerator}{denominator}

    \ln gives \ln instead of ln. Same for \cos

    \sqrt{bla} gives \sqrt{bla}



    Sidenote : that's very good, you put the parenthesis where they needed to be !
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  3. #3
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    you did fine ...

    \ln\left(\frac{\sqrt{x}(1+x^6)}{\cos{x}}\right)
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  4. #4
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    I second guess myself too much I guess.
    Last edited by ThePerfectHacker; September 1st 2008 at 01:16 PM.
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  5. #5
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    Hello, leftyguitarjoe!

    What you did is correct!
    And thank you for showing your work!


    Express as a single logarithm: . \ln(1+x^6) + \frac{1}{2}\ln(x) - \ln(\cos(x))
    I would do it like this . . .

    \ln(1 + x^6) + \ln\left(x^{\frac{1}{2}}\right) - \ln(\cos(x))

    . . = \;\ln\bigg[(1+x^6)x^{\frac{1}{2}}\bigg] - \ln(\cos(x))

    . . = \;\ln\left[\frac{\sqrt{x}\,(1+x^6)}{\cos(x)}\right]

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  6. #6
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    I think its useless if I dont show my work. If I didnt, you wouldnt be able to see where I messed up if I had got it wrong.
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  7. #7
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by leftyguitarjoe View Post
    I think its useless if I dont show my work. If I didnt, you wouldnt be able to see where I messed up if I had got it wrong.
    you wouldn't believe how many students here find that concept difficult to grasp! you deserve that thanks more than you know!
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