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Math Help - Rewriting Logs

  1. #1
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    Rewriting Logs

    I am a little confused on how to rewrite this

    3lnx - 4lnx - 5lnt

    it dosent seem right to right it as

     \ln \frac{\frac{ x^3}{x^4}}{ t^5}
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  2. #2
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    That actually is correct. Just simplify. \frac{x^3}{x^4}=\frac{1}{x}

    So its just \ln \frac{1}{xt^5}

    Or you could just combine like terms before attempting to rewrite it.
    3\ln x-4\ln x=-\ln x
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  3. #3
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    Quote Originally Posted by x5pyd3rx View Post
    I am a little confused on how to rewrite this

    3lnx - 4lnx - 5lnt

    it dosent seem right to right it as

     \ln \frac{\frac{ x^3}{x^4}}{ t^5}
    That's right but it's poor syntax

    \ln(x^3) - \ln(x^4) - \ln(t^5) = \ln \left(\frac{x^3}{x^4t^5}\right) = \ln \left(\frac{x^{-1}}{t^5}\right)  = -\ln \left({xt^{5}}\right)
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  4. #4
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    Smile

    Quote Originally Posted by x5pyd3rx View Post
    I am a little confused on how to rewrite this

    3lnx - 4lnx - 5lnt

    it dosent seem right to right it as

     \ln \frac{\frac{ x^3}{x^4}}{ t^5}
    hi
    3\ln x - 4\ln x - 5\ln t=(\ln x^3-\ln x^4)-\ln t^5=\ln(\frac{x^3}{x^4})-\ln t^5
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  5. #5
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    Quote Originally Posted by x5pyd3rx View Post
    I am a little confused on how to rewrite this

    3lnx - 4lnx - 5lnt

    it dosent seem right to right it as

     \ln \frac{\frac{ x^3}{x^4}}{ t^5}
    3\ln{x} - (4\ln{x} + 5\ln{t})

    \ln(x^3) - \ln(x^4 t^5)

    \ln\left(\frac{x^3}{x^4 t^5}\right)

    \ln\left(\frac{1}{x t^5}\right)

    -\ln(x t^5)
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  6. #6
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    Crap i just got all this help and now i feel stupid because i wrote the problem wrong

    its 3lnx - 4lny -5lnt
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  7. #7
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by x5pyd3rx View Post
    Crap i just got all this help and now i feel stupid because i wrote the problem wrong

    its 3lnx - 4lny -5lnt
    It's pretty much equal to skeeter's second step

    \ln \left(\frac{x^3}{y^4 t^5}\right)
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