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mathivh

  • one year ago

Is this a general rule (-ln...)

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  1. mathivh
    • one year ago
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    Is it generally true that \[\ln(a/b)=-\ln(b/a)\] I have a case in which this equality is correct, but I don't know for sure if this holds for every a,b element of R. My case: \[-\ln \left|\frac{ c-1 }{ c } \right|=\ln \left|\frac{ c }{ c-1 } \right|\]. I don't require a proof, just a simple explanation is fine.

  2. Loser66
    • one year ago
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    the first one is correct. Since ln (a/b) = lna -lnb and ln (b/a) = lnb -lna hence -ln(b/a) = -lnb + lna = lna -lnb = ln (a/b)

  3. Loser66
    • one year ago
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    Not sure about the particular case.

  4. Loser66
    • one year ago
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    ok, let apply |dw:1439242653354:dw|

  5. Loser66
    • one year ago
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    ok, same.

  6. mathivh
    • one year ago
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    Yeah I knew about the particular case, not sure it was correct for every \[a,b \in \mathbb{R}\]. And apparently it does ;-), thanks again. It seems like I'm becoming one of your regular customers!

  7. Loser66
    • one year ago
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    hahaha.... I like the willing-to-study-students. I don't like willing-to-get-the-free-answer-ones. that's why I answer your question.

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